diff --git a/inference-engine/src/low_precision_transformations/src/split.cpp b/inference-engine/src/low_precision_transformations/src/split.cpp
index 486111dd73778a..919c6b5e87b185 100644
--- a/inference-engine/src/low_precision_transformations/src/split.cpp
+++ b/inference-engine/src/low_precision_transformations/src/split.cpp
@@ -111,13 +111,13 @@ void SplitTransformation::updateOutputs(
         updateOutput(context, lastNodes[0], originalNode);
     } else {
         const std::string originalName = originalNode->get_friendly_name();
-        for (auto& lastNode : lastNodes) {
+        for (size_t outIdx = 0; outIdx < lastNodes.size(); ++outIdx) {
             for (size_t i = 0; i < outputSize; ++i) {
                 std::shared_ptr<ngraph::Node> result = context.function->get_output_op(i);
                 std::shared_ptr<ngraph::Node> outputNode = result->get_input_node_shared_ptr(0);
-                if (outputNode.get() == lastNode.get()) {
+                if (outputNode.get() == lastNodes[outIdx].get()) {
                     originalNode->set_friendly_name(originalName + LayerTransformation::originalLayerPostfix);
-                    lastNode->set_friendly_name(originalName + "." + std::to_string(i));
+                    lastNodes[outIdx]->set_friendly_name(originalName + "." + std::to_string(outIdx));
                     break;
                 }
             }
diff --git a/inference-engine/src/low_precision_transformations/src/weightable_layer_transformation.cpp b/inference-engine/src/low_precision_transformations/src/weightable_layer_transformation.cpp
index ce0ae3473d92e5..babcc95303cffe 100644
--- a/inference-engine/src/low_precision_transformations/src/weightable_layer_transformation.cpp
+++ b/inference-engine/src/low_precision_transformations/src/weightable_layer_transformation.cpp
@@ -157,10 +157,15 @@ bool WeightableLayerTransformation::canBeTransformed(const TransformationContext
         }
 
         const size_t outChannelsShapeIndex = is_type<opset1::ConvolutionBackpropData>(layer) ? 1ul : 0ul;
-        if ( // Check if all dimensions of scale except the output channels are all ones
+        if (
+            // expected, it's ok: return true
+            (shape_size(constOutputShape) != 1ul) &&
+            // not expected, something wrong: return false
+            ((constOutputShape.size() <= outChannelsShapeIndex) ||
+            // Check if all dimensions of scale except the output channels are all ones
             (shape_size(constOutputShape) != constOutputShape[outChannelsShapeIndex]) ||
             ((constOutputShape[outChannelsShapeIndex] != 1ul) &&
-                (fqFromWeights->get_output_shape(0)[outChannelsShapeIndex] != constOutputShape[outChannelsShapeIndex]))) {
+                (fqFromWeights->get_output_shape(0)[outChannelsShapeIndex] != constOutputShape[outChannelsShapeIndex])))) {
             return false;
         }
     } else {
diff --git a/inference-engine/tests/functional/inference_engine/lp_transformations/convolution_backprop_data_transformation.cpp b/inference-engine/tests/functional/inference_engine/lp_transformations/convolution_backprop_data_transformation.cpp
index 8e89b952526462..10ba4513f20549 100644
--- a/inference-engine/tests/functional/inference_engine/lp_transformations/convolution_backprop_data_transformation.cpp
+++ b/inference-engine/tests/functional/inference_engine/lp_transformations/convolution_backprop_data_transformation.cpp
@@ -116,6 +116,7 @@ class ConvolutionBackpropDataTransformation : public LayerTransformation, public
         SimpleLowPrecisionTransformer transform;
         transform.add<ngraph::pass::low_precision::ConvolutionBackpropDataTransformation, ngraph::opset1::Convolution>(testValues.params);
         transform.transform(actualFunction);
+
         std::shared_ptr<Node> refWeights = pass::low_precision::fold<opset1::Broadcast>(
                 testValues.expected.weights,
                 opset1::Constant::create(
@@ -202,6 +203,26 @@ const std::vector<ConvolutionBackpropDataTransformationTestValues> testValues =
             true
         }
     },
+    // with zero point
+    {
+        LayerTransformation::createParamsU8I8(),
+        // ActualValues
+        {
+            ngraph::element::u8,
+            {{ngraph::element::f32}, { 128.f }, { 0.02f }},
+            { 255ul, Shape({}), { 0.f }, { 254.f }, { -1.27f }, { 1.27f } },
+            op::Constant::create(ngraph::element::i8, ngraph::Shape{}, std::vector<float>{ 2.f })
+        },
+        // ExpectedValues
+        {
+            ngraph::element::u8,
+            {{}, { { 128.f }, ngraph::element::f32, {}, false }, {}},
+            {},
+            {{}, {}, {{ 0.0002f }, ngraph::element::f32, { 1 }}},
+            op::Constant::create(ngraph::element::i8, ngraph::Shape{}, std::vector<float>{ -125.f }),
+            true
+        }
+    },
     // updatePrecisions = false
     {
         LayerTransformation::createParamsU8I8().setUpdatePrecisions(false),
@@ -262,6 +283,26 @@ const std::vector<ConvolutionBackpropDataTransformationTestValues> testValues =
             true
         }
     },
+    // without zero point
+    {
+        LayerTransformation::createParamsU8I8(),
+        // ActualValues
+        {
+            ngraph::element::u8,
+            {{ngraph::element::f32}, {}, { 0.02f }},
+            { 255ul, Shape({}), { 0.f }, { 254.f }, { -1.27f }, { 1.27f } },
+            op::Constant::create(ngraph::element::i8, ngraph::Shape{}, std::vector<float>{ 2.f })
+        },
+        // ExpectedValues
+        {
+            ngraph::element::u8,
+            {},
+            {},
+            {{}, {}, {{ 0.0002f }, ngraph::element::f32, { 1 }}},
+            op::Constant::create(ngraph::element::i8, ngraph::Shape{}, std::vector<float>{ -125.f }),
+            true
+        }
+    },
     // QDq version
     {
         LayerTransformation::createParamsU8I8(),
diff --git a/inference-engine/tests/functional/plugin/cpu/shared_tests_instances/low_precision_transformations/convolution_backprop_data_transformation.cpp b/inference-engine/tests/functional/plugin/cpu/shared_tests_instances/low_precision_transformations/convolution_backprop_data_transformation.cpp
index a6e2e93a37ebb8..223f9743a61888 100644
--- a/inference-engine/tests/functional/plugin/cpu/shared_tests_instances/low_precision_transformations/convolution_backprop_data_transformation.cpp
+++ b/inference-engine/tests/functional/plugin/cpu/shared_tests_instances/low_precision_transformations/convolution_backprop_data_transformation.cpp
@@ -27,6 +27,13 @@ const std::vector<LayerTestsDefinitions::ConvolutionBackpropDataTransformationPa
         "U8"
     },
     // FQ on weights
+    {
+        {256ul, ngraph::Shape{}, { 0.f }, { 25.5f }, { 0.f }, { 25.5f }},
+        {255ul, ngraph::Shape{}, { -12.7f }, { 12.7f }, { -12.7f }, { 12.7f }},
+        "convolutionBackpropData_original",
+        "U8"
+    },
+    // FQ on weights
     // with zero point
     {
         {256ul, ngraph::Shape{1, 1, 1, 1}, { 0.f }, { 255.f }, { -12.7f }, { 12.8f }},
diff --git a/inference-engine/tests/functional/plugin/cpu/shared_tests_instances/low_precision_transformations/convolution_transformation.cpp b/inference-engine/tests/functional/plugin/cpu/shared_tests_instances/low_precision_transformations/convolution_transformation.cpp
index 086a2ef6f16a29..594e645980aa74 100644
--- a/inference-engine/tests/functional/plugin/cpu/shared_tests_instances/low_precision_transformations/convolution_transformation.cpp
+++ b/inference-engine/tests/functional/plugin/cpu/shared_tests_instances/low_precision_transformations/convolution_transformation.cpp
@@ -46,6 +46,14 @@ const std::vector<LayerTestsDefinitions::ConvolutionTransformationParam> params
         "Convolution",
         "U8"
     },
+    {
+        { 256ul, ngraph::Shape {}, { 0.f }, { 255.f }, { 0.f }, { 25.5f } },
+        false,
+        { 255ul, ngraph::Shape {}, { 0.f }, { 254.f }, { -12.7f }, { 12.7f } },
+        false,
+        "Convolution",
+        "U8"
+    },
     {
         { 16ul, ngraph::Shape { 1, 1, 1, 1 }, { 0.f }, { 255.f }, { 0.f }, { 25.5f } },
         false,
diff --git a/inference-engine/tests/functional/plugin/gpu/shared_tests_instances/low_precision_transformations/convolution_backprop_data_transformation.cpp b/inference-engine/tests/functional/plugin/gpu/shared_tests_instances/low_precision_transformations/convolution_backprop_data_transformation.cpp
index 2cf625b58628a6..697059e3ce24bf 100644
--- a/inference-engine/tests/functional/plugin/gpu/shared_tests_instances/low_precision_transformations/convolution_backprop_data_transformation.cpp
+++ b/inference-engine/tests/functional/plugin/gpu/shared_tests_instances/low_precision_transformations/convolution_backprop_data_transformation.cpp
@@ -28,6 +28,13 @@ const std::vector<LayerTestsDefinitions::ConvolutionBackpropDataTransformationPa
         "U8"
     },
     // FQ on weights
+    {
+        {256ul, ngraph::Shape{}, { 0.f }, { 25.5f }, { 0.f }, { 25.5f }},
+        {255ul, ngraph::Shape{}, { -12.7f }, { 12.7f }, { -12.7f }, { 12.7f }},
+        "convolutionBackpropData_original",
+        "U8"
+    },
+    // FQ on weights
     {
         {256ul, ngraph::Shape{1, 1, 1, 1}, { -12.8f }, { 12.7f }, { -12.8f }, { 12.7f }},
         {255ul, ngraph::Shape{1, 1, 1, 1}, { -12.7f }, { 12.7f }, { -12.7f }, { 12.7f }},
diff --git a/inference-engine/tests/functional/plugin/gpu/shared_tests_instances/low_precision_transformations/convolution_transformation.cpp b/inference-engine/tests/functional/plugin/gpu/shared_tests_instances/low_precision_transformations/convolution_transformation.cpp
index ce0db6e1e6681d..2a0c8ff14fc7ac 100644
--- a/inference-engine/tests/functional/plugin/gpu/shared_tests_instances/low_precision_transformations/convolution_transformation.cpp
+++ b/inference-engine/tests/functional/plugin/gpu/shared_tests_instances/low_precision_transformations/convolution_transformation.cpp
@@ -46,6 +46,14 @@ const std::vector<LayerTestsDefinitions::ConvolutionTransformationParam> params
         "Convolution",
         "U8"
     },
+    {
+        { 256ul, ngraph::Shape {}, { 0.f }, { 255.f }, { 0.f }, { 25.5f } },
+        false,
+        { 255ul, ngraph::Shape {}, { 0.f }, { 254.f }, { -12.7f }, { 12.7f } },
+        false,
+        "Convolution",
+        "U8"
+    },
     {
         { 256ul, ngraph::Shape { 1, 1, 1, 1 }, { 0.f }, { 255.f }, { -12.75f }, { 6.375f } },
         true,