diff --git a/tket/src/CMakeLists.txt b/tket/src/CMakeLists.txt
index 03ed3e3333..7871017f9e 100644
--- a/tket/src/CMakeLists.txt
+++ b/tket/src/CMakeLists.txt
@@ -212,6 +212,7 @@ set(TKET_SOURCES
     ${TKET_TRANSFORM_DIR}/MeasurePass.cpp
     ${TKET_TRANSFORM_DIR}/ContextualReduction.cpp
     ${TKET_TRANSFORM_DIR}/ThreeQubitSquash.cpp
+    ${TKET_TRANSFORM_DIR}/CZReordering.cpp
 
     # Routing
     ${TKET_ROUTING_DIR}/Qubit_Placement.cpp
diff --git a/tket/src/Transformations/CZReordering.cpp b/tket/src/Transformations/CZReordering.cpp
new file mode 100644
index 0000000000..d4724c461c
--- /dev/null
+++ b/tket/src/Transformations/CZReordering.cpp
@@ -0,0 +1,59 @@
+// Copyright 2019-2021 Cambridge Quantum Computing
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "Transform.hpp"
+
+namespace tket {
+
+    // For a gate vertex and an edge, traverse back to find the associated input vertex.
+    Vertex get_input_from_vertex_edge(Circuit &circ, const Vertex &current_vertex, const Edge &current_outedge) {
+        Edge current_e = current_outedge;
+        Vertex current_v = current_vertex; 
+        while (true) {
+            if (is_initial_q_type(circ.get_OpType_from_Vertex(current_v))) {
+                return current_v;
+            }
+            std::tie(current_v, current_e) = circ.get_prev_pair(current_v, current_e);
+        }
+    }
+    // Assume the circuit only contains CZ gates as the two qubit gate
+    Transform Transform::reorder_cz(const ArchitecturePtr& architecture) {
+        return Transform([architecture](Circuit &circ) {
+            bool success = false;
+            BGL_FORALL_VERTICES(vert, circ.dag, DAG) {
+                if (circ.get_OpType_from_Vertex(vert) == OpType::CZ)
+                {
+                    // Check if this operation is valid
+                    Vertex input_1 = get_input_from_vertex_edge(circ, vert, circ.get_nth_out_edge(vert, 0));
+                    Vertex input_2 = get_input_from_vertex_edge(circ, vert, circ.get_nth_out_edge(vert, 1));
+                    UnitID q_1 = circ.get_id_from_in(input_1);
+                    UnitID q_2 = circ.get_id_from_in(input_2);
+                    if (architecture->valid_operation({Node(q_1), Node(q_2)})) {
+                        // Remove the vertex
+                        circ.remove_vertex(
+                                        vert, Circuit::GraphRewiring::Yes,
+                                        Circuit::VertexDeletion::No);
+                        // Get input edges for in_q and out_q
+                        Edge edge_1 = circ.get_nth_out_edge(input_1, 0);
+                        Edge edge_2 = circ.get_nth_out_edge(input_2, 0);
+                        // Move the gate to the front
+                        circ.rewire(vert, {edge_1, edge_2}, {EdgeType::Quantum, EdgeType::Quantum});
+                        success = true;
+                    }
+                }
+            }
+            return success;
+        });
+    }
+}   // namespace tket
\ No newline at end of file
diff --git a/tket/src/Transformations/Transform.hpp b/tket/src/Transformations/Transform.hpp
index 06bed251ea..13c08c8a22 100644
--- a/tket/src/Transformations/Transform.hpp
+++ b/tket/src/Transformations/Transform.hpp
@@ -542,6 +542,11 @@ class Transform {
    */
   static Transform simplify_measured();
 
+  ///////////////
+  // Reordering CZ//
+  ///////////////
+  static Transform reorder_cz(const ArchitecturePtr& architecture);
+
   ///////////////////////////////////////////////
   // Minor components for other Transform passes//
   ///////////////////////////////////////////////
diff --git a/tket/tests/test_ReorderingCZ.cpp b/tket/tests/test_ReorderingCZ.cpp
new file mode 100644
index 0000000000..6d774978a6
--- /dev/null
+++ b/tket/tests/test_ReorderingCZ.cpp
@@ -0,0 +1,37 @@
+#include <catch2/catch.hpp>
+#include "Transformations/Transform.hpp"
+
+namespace tket {
+    SCENARIO("Test Transform::reorder_cz") {
+    std::vector<Node> nodes = {Node("test_node", 0), Node("test_node", 1),
+                             Node("test_node", 2), Node("node_test", 3)};
+    
+    // n0 -- n1 -- n2 -- n3
+    Architecture architecture(
+      {{nodes[0], nodes[1]},
+       {nodes[1], nodes[2]},
+       {nodes[2], nodes[3]}});
+    ArchitecturePtr shared_arc = std::make_shared<Architecture>(architecture);
+    Circuit circ(4);
+    std::vector<Qubit> qubits = circ.all_qubits();
+    // Physically invalid operations
+    circ.add_op<UnitID>(OpType::CZ, {qubits[0], qubits[2]});
+    circ.add_op<UnitID>(OpType::CZ, {qubits[0], qubits[3]});
+    // Physically valid operations
+    circ.add_op<UnitID>(OpType::CZ, {qubits[0], qubits[1]});
+    circ.add_op<UnitID>(OpType::CZ, {qubits[2], qubits[3]});
+    std::map<UnitID, UnitID> rename_map = {
+        {qubits[0], nodes[0]}, {qubits[1], nodes[1]}, {qubits[2], nodes[2]},
+        {qubits[3], nodes[3]}};
+    circ.rename_units(rename_map);
+    std::cout<<circ;
+    Transform::reorder_cz(shared_arc).apply(circ);
+    std::cout<<circ;
+    std::vector<Command> commands = circ.get_commands();
+    Command c0 = commands[0];
+    Command c1 = commands[1];
+    REQUIRE(shared_arc->valid_operation({Node(c0.get_args()[0]), Node(c0.get_args()[1])}));
+    REQUIRE(shared_arc->valid_operation({Node(c1.get_args()[0]), Node(c1.get_args()[1])}));
+    
+}
+}
\ No newline at end of file
diff --git a/tket/tests/tkettestsfiles.cmake b/tket/tests/tkettestsfiles.cmake
index b5dd764afc..551df817d4 100644
--- a/tket/tests/tkettestsfiles.cmake
+++ b/tket/tests/tkettestsfiles.cmake
@@ -23,6 +23,7 @@ set(TEST_SOURCES
     ${TKET_TESTS_DIR}/tests_main.cpp
     ${TKET_TESTS_DIR}/testutil.cpp
     ${TKET_TESTS_DIR}/CircuitsForTesting.cpp
+    ${TKET_TESTS_DIR}/test_ReorderingCZ.cpp
     ${TKET_TESTS_DIR}/Utils/test_MatrixAnalysis.cpp
     ${TKET_TESTS_DIR}/Utils/test_CosSinDecomposition.cpp
     ${TKET_TESTS_DIR}/Graphs/EdgeSequence.cpp