diff --git a/lib/lierep.gd b/lib/lierep.gd
index cc97469ed0..c92fe687c7 100644
--- a/lib/lierep.gd
+++ b/lib/lierep.gd
@@ -549,7 +549,7 @@ DeclareOperation( "DominantCharacter", [ IsRootSystem, IsList ] );
 ##  with highest weight <M>w_i</M> for <M>i = 1, 2</M>.
 ##  Let <M>W = V_1 \otimes V_2</M>.
 ##  Then in general <M>W</M> is a reducible <A>L</A>-module. Now this function
-##  returns a list of two lists. The first of these is the list of highest
+##  returns a list of two lists. The first of these is the sorted list of highest
 ##  weights of the irreducible modules occurring in the decomposition of
 ##  <M>W</M> as a direct sum of irreducible modules. The second list contains
 ##  the multiplicities of these weights (i.e., the number of copies of
@@ -587,8 +587,8 @@ DeclareOperation( "DecomposeTensorProduct", [ IsLieAlgebra, IsList, IsList ] );
 ##  [ [ [ 1, 1, 0, 0 ], [ 2, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 1, 0, 0 ], 
 ##        [ 1, 0, 0, 0 ], [ 0, 0, 0, 0 ] ], [ 1, 1, 4, 6, 14, 21 ] ]
 ##  gap> DecomposeTensorProduct( L, [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ] );
-##  [ [ [ 1, 0, 1, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 1, 0, 0 ], 
-##        [ 2, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 1, 1, 0, 0 ] ], 
+##  [ [ [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ], 
+##        [ 1, 0, 1, 0 ], [ 1, 1, 0, 0 ], [ 2, 0, 0, 0 ] ],
 ##    [ 1, 1, 1, 1, 1, 1, 1 ] ]
 ##  gap> DimensionOfHighestWeightModule( L, [ 1, 2, 3, 4 ] );
 ##  79316832731136
diff --git a/lib/lierep.gi b/lib/lierep.gi
index dfea0bbade..4af3fc71ce 100644
--- a/lib/lierep.gi
+++ b/lib/lierep.gi
@@ -1306,10 +1306,10 @@ InstallMethod( DecomposeTensorProduct,
 
                 nu:= mu[1]-rho;
                 mult:= ch1[2][i]*( (-1)^Length(mu[2]) );
-                p:= Position( wts, nu );
-                if p = fail then
-                    Add( wts, nu );
-                    Add( mlts, mult );
+                p:= PositionSorted( wts, nu );
+                if not IsBound( wts[p] ) or wts[p] <> nu then
+                    Add( wts, nu, p );
+                    Add( mlts, mult, p );
                 else
                     mlts[p]:= mlts[p]+mult;
                     if mlts[p] = 0 then
diff --git a/tst/testinstall/algsc.tst b/tst/testinstall/algsc.tst
index d0c9cd0c56..d8d06de8f4 100644
--- a/tst/testinstall/algsc.tst
+++ b/tst/testinstall/algsc.tst
@@ -1,6 +1,7 @@
 #@local T0,T1,T2,T3,a,b,c,coeff,der,e,fam,g,gens,i,id,j,k,l1,l2,l3,lcs,orb
 #@local TestMonomialUseLattice_Orig,permgrp,ps,q,s,s1,s2,s3,sc,t,theta
 #@local U,ucs,v,vecs,vectors,w,z,A,V,W
+#@local L,l
 gap> START_TEST("algsc.tst");
 
 #############################################################################
@@ -218,6 +219,34 @@ gap> LieCentralizer( l1, ps );
 gap> LieNormalizer( l1, ps );
 <Lie algebra of dimension 4 over Rationals>
 
+# Test added for DecomposeTensorProduct
+gap> L := SimpleLieAlgebra( "A", 3, Rationals );;
+gap> v := [1,3,1];;
+gap> w := [4,1,4];;
+gap> l := DecomposeTensorProduct( L, v, w );
+[ [ [ 0, 0, 8 ], [ 0, 1, 6 ], [ 0, 2, 4 ], [ 0, 2, 8 ], [ 0, 3, 2 ], 
+      [ 0, 3, 6 ], [ 0, 4, 0 ], [ 0, 4, 4 ], [ 0, 5, 2 ], [ 0, 6, 0 ], 
+      [ 1, 0, 5 ], [ 1, 0, 9 ], [ 1, 1, 3 ], [ 1, 1, 7 ], [ 1, 2, 1 ], 
+      [ 1, 2, 5 ], [ 1, 3, 3 ], [ 1, 3, 7 ], [ 1, 4, 1 ], [ 1, 4, 5 ], 
+      [ 1, 5, 3 ], [ 1, 6, 1 ], [ 2, 0, 6 ], [ 2, 1, 4 ], [ 2, 1, 8 ], 
+      [ 2, 2, 2 ], [ 2, 2, 6 ], [ 2, 3, 0 ], [ 2, 3, 4 ], [ 2, 4, 2 ], 
+      [ 2, 4, 6 ], [ 2, 5, 0 ], [ 2, 5, 4 ], [ 2, 6, 2 ], [ 3, 0, 3 ], 
+      [ 3, 0, 7 ], [ 3, 1, 1 ], [ 3, 1, 5 ], [ 3, 2, 3 ], [ 3, 2, 7 ], 
+      [ 3, 3, 1 ], [ 3, 3, 5 ], [ 3, 4, 3 ], [ 3, 5, 1 ], [ 3, 5, 5 ], 
+      [ 3, 6, 3 ], [ 4, 0, 4 ], [ 4, 0, 8 ], [ 4, 1, 2 ], [ 4, 1, 6 ], 
+      [ 4, 2, 0 ], [ 4, 2, 4 ], [ 4, 3, 2 ], [ 4, 3, 6 ], [ 4, 4, 0 ], 
+      [ 4, 4, 4 ], [ 4, 5, 2 ], [ 5, 0, 1 ], [ 5, 0, 5 ], [ 5, 1, 3 ], 
+      [ 5, 1, 7 ], [ 5, 2, 1 ], [ 5, 2, 5 ], [ 5, 3, 3 ], [ 5, 4, 1 ], 
+      [ 5, 4, 5 ], [ 5, 5, 3 ], [ 6, 0, 2 ], [ 6, 0, 6 ], [ 6, 1, 0 ], 
+      [ 6, 1, 4 ], [ 6, 2, 2 ], [ 6, 2, 6 ], [ 6, 3, 0 ], [ 6, 3, 4 ], 
+      [ 6, 4, 2 ], [ 7, 0, 3 ], [ 7, 1, 1 ], [ 7, 1, 5 ], [ 7, 2, 3 ], 
+      [ 7, 3, 1 ], [ 8, 0, 0 ], [ 8, 0, 4 ], [ 8, 1, 2 ], [ 8, 2, 0 ], 
+      [ 9, 0, 1 ] ], 
+  [ 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 1, 1, 4, 1, 5, 5, 1, 4, 2, 2, 1, 3, 4, 
+      2, 4, 5, 2, 6, 5, 1, 2, 2, 1, 1, 3, 1, 6, 7, 2, 5, 5, 5, 2, 1, 1, 3, 1, 
+      4, 4, 2, 7, 6, 2, 2, 4, 2, 1, 3, 6, 1, 5, 4, 5, 2, 1, 1, 3, 1, 2, 4, 5, 
+      1, 2, 2, 1, 3, 4, 1, 2, 1, 1, 1, 2, 1, 1 ] ]
+
 # use AsAlgebra etc.
 gap> KappaPerp( l1, ps );
 <vector space of dimension 6 over Rationals>