diff --git a/docs/src/Groups/action.md b/docs/src/Groups/action.md
index f36dd704da9..abf584b3a96 100644
--- a/docs/src/Groups/action.md
+++ b/docs/src/Groups/action.md
@@ -40,7 +40,7 @@ on_sets
 permuted
 on_indeterminates
 on_lines
-on_rref_mats
+on_echelon_form_mats
 on_subgroups
 ```
 
diff --git a/src/Groups/action.jl b/src/Groups/action.jl
index 6a516a983d6..6398215f160 100644
--- a/src/Groups/action.jl
+++ b/src/Groups/action.jl
@@ -456,18 +456,18 @@ on_subgroups(x::T, g::GAPGroupElem) where T <: GAPGroup = T(on_subgroups(GapObj(
 
 
 @doc raw"""
-    on_rref_mats(m::MatElem{T}, x::MatrixGroupElem) where T <: FinFieldElem
+    on_echelon_form_mats(m::MatElem{T}, x::MatrixGroupElem) where T <: FinFieldElem
 
 Return the image of `m` under `x`,
 where the action is given by first computing the product `m * x`
-and then normalizing the result by computing its reduced row echelon form,
-see [`rref(M::MatrixElem{T})`](@ref).
+and then normalizing the result by computing its reduced row echelon form
+with `echelon_form`.
 
 Identifying `m` with the subspace of the natural module for the group of `x`
 that is generated by the rows of `m`,
-`on_rref_mats` describes the action on subspaces of this natural module.
-Note that for computing the orbit and stabilizer of `m` w.r.t. `on_rref_mats`,
-`m` must be in reduced row echelon form.
+`on_echelon_form_mats` describes the action on subspaces of this natural module.
+Note that for computing the orbit and stabilizer of `m` w.r.t.
+`on_echelon_form_mats`, `m` must be in reduced row echelon form.
 
 # Examples
 ```jldoctest
@@ -482,15 +482,15 @@ julia> m = matrix(embW)
 [1   0   0]
 [0   0   1]
 
-julia> S, _ = stabilizer(G, m, on_rref_mats);  order(S)
+julia> S, _ = stabilizer(G, m, on_echelon_form_mats);  order(S)
 24
 
-julia> orb = orbit(G, on_rref_mats, m);  length(orb)
+julia> orb = orbit(G, on_echelon_form_mats, m);  length(orb)
 7
 ```
 """
-function on_rref_mats(m::MatElem{T}, x::MatrixGroupElem) where T <: FinFieldElem
-  return rref(m * x)[2]
+function on_echelon_form_mats(m::MatElem{T}, x::MatrixGroupElem) where T <: FinFieldElem
+  return echelon_form(m * x)[2]
 end
 
 @doc raw"""
diff --git a/src/exports.jl b/src/exports.jl
index 692069e559f..175896bef0c 100644
--- a/src/exports.jl
+++ b/src/exports.jl
@@ -1172,7 +1172,7 @@ export objective_function
 export omega_group
 export on_indeterminates
 export on_lines
-export on_rref_mats
+export on_echelon_form_mats
 export on_sets
 export on_sets_sets
 export on_simplicial_complex