diff --git a/lib/recognition_new.gi b/lib/recognition_new.gi
index 5fb035e..e91f7c7 100644
--- a/lib/recognition_new.gi
+++ b/lib/recognition_new.gi
@@ -125,13 +125,10 @@ InstallGlobalFunction( ClassicalForms_GeneratorsWithBetterScalarsSesquilinear,
         if IsList(a1) then
             root := NthRoot(field,a1[2],a1[1]);
             if a1[1] = 1 then # the matrix m1 has scalar a1[2]
-                #if a1[2] has a square root, we can replace m1 with m1*sqrt{a1[2]};
-                if LogFFE(a1[2],PrimitiveRoot(field)) mod 2 = 0 then
-                    return [m1/NthRoot(field,a1[2],2),[One(field)]];
+                if LogFFE(a1[2],PrimitiveRoot(field)) mod (q+1) = 0 then
+                    return [m1/NthRoot(field,a1[2],q+1),[One(field)]];
                 fi;
-                return [m1,[a1[2]]]; #originally, the three lines above this return were not there. Those three lines make sure scalar becomes 1 if possible (basicaly if there is a sqrt).
-            elif LogFFE(root,PrimitiveRoot(field)) mod (q+1) = 0 then
-                return [m1/NthRoot(field,root,q+1),[One(field)]]; #either frob = id, then q+1 = 2, or frob is not trivial, then we take q+1-st root. In both cases, modify m1 to a matrix that has scalar one.
+                return [m1,[a1[2]]]; #originally, the three lines above this return were not there. Those three lines make sure scalar becomes 1 if possible (basically if there is a q+1-st root).
             else
                 scalars := AsList(Group(NthRoot(field,a1[2],a1[1]))); # add all possible scalars for m1
                 if count = 0 then
diff --git a/tst/adv/test_pres_sesforms3.tst b/tst/adv/test_pres_sesforms3.tst
new file mode 100644
index 0000000..4509298
--- /dev/null
+++ b/tst/adv/test_pres_sesforms3.tst
@@ -0,0 +1,81 @@
+gap> START_TEST("Forms: test_pres_sesforms3.tst");
+
+# Regression tests for issue #83:
+# examples where sesquilinear forms preserved up to scalars
+# were not detected due to scalar normalization issues.
+gap> grp := Group([
+> [ [  Z(3^2)^3,  Z(3^2)^6,  Z(3^2)^7 ],
+>   [  Z(3^2)^7,  Z(3^2)^2,    Z(3)^0 ],
+>   [  Z(3^2)^7,  Z(3^2)^7,    0*Z(3) ] ],
+> [ [    0*Z(3),    0*Z(3),      Z(3) ],
+>   [  Z(3^2)^7,    Z(3)^0,  Z(3^2)^7 ],
+>   [      Z(3),    Z(3^2),      Z(3) ] ],
+> [ [    Z(3^2),    0*Z(3),    0*Z(3) ],
+>   [    0*Z(3),    Z(3^2),    0*Z(3) ],
+>   [    0*Z(3),    0*Z(3),    Z(3^2) ] ]
+> ]);;
+gap> forms := PreservedSesquilinearForms(grp);
+[ < hermitian form > ]
+gap> TestPreservedSesquilinearForms(grp, forms);
+true
+gap> grp := Group(Z(3)^0*[
+> [ [ 0, 1, 2, 2, 0, 1, 1, 0 ],
+>   [ 0, 1, 0, 2, 0, 1, 0, 2 ], 
+>   [ 1, 2, 2, 0, 0, 0, 2, 2 ], 
+>   [ 0, 0, 0, 1, 0, 0, 0, 0 ], 
+>   [ 0, 0, 0, 0, 1, 0, 1, 1 ],
+>   [ 0, 0, 0, 0, 0, 0, 0, 1 ],
+>   [ 0, 0, 0, 0, 0, 1, 1, 2 ],
+>   [ 0, 0, 0, 0, 0, 2, 0, 2 ] ],
+> [ [ 2, 1, 0, 2, 2, 2, 0, 1 ],
+>   [ 0, 0, 0, 1, 0, 2, 2, 1 ],
+>   [ 1, 2, 0, 0, 1, 0, 2, 2 ],
+>   [ 0, 0, 0, 1, 0, 1, 2, 1 ], 
+>   [ 1, 0, 2, 1, 1, 1, 0, 0 ],
+>   [ 0, 1, 0, 2, 1, 1, 1, 1 ],
+>   [ 1, 2, 1, 0, 0, 0, 2, 2 ],
+>   [ 0, 1, 0, 1, 1, 1, 2, 2 ] ],
+> [ [ 0, 2, 0, 1, 1, 2, 1, 0 ],
+>   [ 2, 0, 1, 2, 2, 1, 0, 2 ],
+>   [ 2, 2, 0, 0, 0, 0, 2, 1 ],
+>   [ 1, 1, 1, 1, 0, 0, 1, 2 ], 
+>   [ 1, 1, 2, 0, 2, 0, 1, 2 ],
+>   [ 0, 2, 0, 1, 2, 0, 2, 0 ],
+>   [ 1, 0, 1, 2, 2, 1, 0, 1 ],
+>   [ 0, 2, 0, 2, 2, 1, 1, 0 ] ]
+> ]);;
+gap> forms := PreservedSesquilinearForms(grp);
+[ < bilinear form > ]
+gap> TestPreservedSesquilinearForms(grp, forms);
+true
+gap> grp := Group(Z(5)^0*[
+> [ [ 0, 1, 0, 0, 0, 0, 0, 0 ],
+>   [ 0, 0, 0, 0, 1, 0, 0, 0 ],
+>   [ 0, 0, 0, 0, 0, 0, 0, 1 ],
+>   [ 2, 3, 4, 3, 1, 3, 2, 4 ],
+>   [ 1, 4, 0, 0, 1, 0, 0, 0 ],
+>   [ 0, 2, 2, 2, 4, 4, 2, 1 ],
+>   [ 2, 3, 4, 2, 1, 3, 3, 4 ],
+>   [ 2, 2, 3, 0, 1, 0, 0, 3 ] ],
+> [ [ 0, 0, 1, 0, 0, 0, 0, 0 ],
+>   [ 0, 0, 0, 0, 0, 1, 0, 0 ],
+>   [ 2, 4, 0, 3, 2, 1, 2, 2 ],
+>   [ 2, 4, 0, 2, 4, 4, 4, 4 ],
+>   [ 4, 4, 1, 0, 1, 0, 3, 2 ],
+>   [ 1, 1, 2, 3, 2, 4, 1, 3 ],
+>   [ 3, 2, 0, 3, 1, 4, 1, 4 ],
+>   [ 3, 3, 1, 4, 0, 3, 4, 3 ] ],
+> [ [ 0, 0, 0, 1, 0, 0, 0, 0 ],
+>   [ 0, 0, 0, 0, 0, 0, 1, 0 ],
+>   [ 2, 2, 3, 1, 3, 3, 2, 4 ],
+>   [ 3, 0, 0, 0, 0, 0, 0, 0 ],
+>   [ 1, 0, 2, 1, 0, 3, 2, 1 ],
+>   [ 1, 3, 2, 4, 3, 1, 2, 2 ],
+>   [ 0, 3, 0, 0, 0, 0, 0, 0 ],
+>   [ 0, 1, 3, 0, 3, 1, 0, 1 ] ]
+> ]);;
+gap> forms := PreservedSesquilinearForms(grp);
+[ < bilinear form > ]
+gap> TestPreservedSesquilinearForms(grp, forms);
+true
+gap> STOP_TEST("test_pres_sesforms3.tst", 10000 );