diff --git a/lib/stbcbckt.gi b/lib/stbcbckt.gi
index 772e274de4..6b54b383cf 100644
--- a/lib/stbcbckt.gi
+++ b/lib/stbcbckt.gi
@@ -2960,8 +2960,8 @@ local   Omega,  P,  rbase,  L,mg,mh,i;
     mh:=MovedPoints(H);
     Omega := Intersection(mg,mh);
 
-    # disjoint?
-    if Length(Omega)=0 then
+    # no two points moved in common?
+    if Length(Omega)<=1 then
       return TrivialSubgroup(Parent(G));
     fi;
 
diff --git a/tst/testinstall/stbcbckt.tst b/tst/testinstall/stbcbckt.tst
new file mode 100644
index 0000000000..b596361eca
--- /dev/null
+++ b/tst/testinstall/stbcbckt.tst
@@ -0,0 +1,11 @@
+#@local G,p
+gap> START_TEST("stbcbckt.tst");
+
+# Intersection for perm groups with a single moved point in common
+gap> G := Group(GeneratorsOfGroup(SymmetricGroup(100)));;
+gap> p := PermList(Concatenation([100 .. 199], [1 .. 99]));;
+gap> IsTrivial(Intersection(G, G ^ p));
+true
+
+#
+gap> STOP_TEST("stbcbckt.tst", 1);