diff --git a/gap/base/recognition.gi b/gap/base/recognition.gi
index 2a4da978..ea524ed8 100644
--- a/gap/base/recognition.gi
+++ b/gap/base/recognition.gi
@@ -691,33 +691,52 @@ InstallGlobalFunction( RecogniseGeneric,
                  depth,").");
             done := ImmediateVerification(ri);
         fi;
-    until done;
-
-    # Set nice generators and CalcStdPresentation of ri
-    SetNiceGens(ri,Concatenation(pregensfac(ri), NiceGens(riker)));
-    if not HasStdPresentation(ri) and not HasCalcStdPresentation(ri) then
-        SetCalcStdPresentation(ri,CalcStdPresentationGenericNonLeaf);
-    fi;
+        if done then
+            # Set nice generators and CalcStdPresentation of ri
+            SetNiceGens(ri,Concatenation(pregensfac(ri), NiceGens(riker)));
+            if not HasStdPresentation(ri) and not HasCalcStdPresentation(ri) then
+                SetCalcStdPresentation(ri,CalcStdPresentationGenericNonLeaf);
+            fi;
 
-    # Check that all (input) generators of H lie in the group generated by
-    # the nice generators.
-    # One could argue that this step should only be performed if verification is desired,
-    # but [BHLO15, 5.2 (6)] suggests to always do this.
-    # In any case, it should be relatively cheap.
-    # Note that without this step, the success of CalcStdPresentation is not sufficient
-    # to guarantee verification, even if this is not clear from [BHLO15, 4.3, 4.5, 5.3.1].
-    for h in GeneratorsOfGroup( H ) do
-        if SLPforElement(ri, h) = fail then
-            # NiceGens(ri) is too small, abort
-            if InfoLevel(InfoRecog) = 1 and depth = 0 then Print("\n"); fi;
-            Info(
-                InfoRecog, 1,
-                "RecogNode <ri> could not be recognised,",
-                " IsReady(<ri>) is not set, recognition aborts"
-            );
-            return ri;
+            # Check that all (input) generators of H lie in the group generated
+            # by the nice generators.  If a generator reveals an additional
+            # kernel element, add it and retry kernel recognition.
+            for i in [1..Length(GeneratorsOfGroup( H ))] do
+                h := GeneratorsOfGroup( H )[i];
+                if SLPforElement(ri, h) = fail then
+                    x := ImageElm(Homom(ri), h);
+                    if x <> fail then
+                        s := SLPforElement(ImageRecogNode(ri), x);
+                    else
+                        s := fail;
+                    fi;
+                    if s <> fail then
+                        y := ResultOfStraightLineProgram(s, ri!.pregensfacwithmem);
+                        z := ri!.gensHmem[i] * y^-1;
+                        if not isone(ri)(z) and
+                           not ForAny(gensN(ri), x -> isequal(ri)(x, z)) then
+                            Add(gensN(ri), z);
+                            Info(InfoRecog, 2,
+                                 "Final verification found extra kernel ",
+                                 "element (depth=", depth, ").");
+                            done := false;
+                        fi;
+                    fi;
+                    if done then
+                        # NiceGens(ri) is too small, abort
+                        if InfoLevel(InfoRecog) = 1 and depth = 0 then
+                            Print("\n");
+                        fi;
+                        Info(InfoRecog, 1,
+                             "RecogNode <ri> could not be recognised,",
+                             " IsReady(<ri>) is not set, recognition aborts");
+                        return ri;
+                    fi;
+                    break;
+                fi;
+            od;
         fi;
-    od;
+    until done;
 
     if InfoLevel(InfoRecog) = 1 and depth = 0 then Print("\n"); fi;
     # StopStoringRandEls(ri);
diff --git a/tst/working/quick/bugfix.tst b/tst/working/quick/bugfix.tst
index f5825d12..5f612728 100644
--- a/tst/working/quick/bugfix.tst
+++ b/tst/working/quick/bugfix.tst
@@ -440,6 +440,18 @@ gap> Size(ri);
 gap> IsCorrect(ri);
 true
 
+# The top-level GoProjective kernel recognition can initially sample only a
+# proper subgroup of the scalar kernel. Final generator verification must retry
+# the kernel after adding the missing residual kernel element.
+gap> seed:=234;; Reset(GlobalMersenneTwister,seed);; Reset(GlobalRandomSource,seed);;
+gap> h := GL(19,5);;
+gap> g := GroupWithGenerators(ProductReplacer(h)!.team);;
+gap> ri := RECOG.TestGroup(g,false,Size(h));;
+gap> IsReady(ri);
+true
+gap> Size(ri) = Size(GL(19,5));
+true
+
 #
 gap> SetInfoLevel(InfoRecog, oldInfoLevel);
 gap> STOP_TEST("bugfix.tst");