diff --git a/spot/tl/formula.cc b/spot/tl/formula.cc
index ab01b15f5..f6f4dbcfa 100644
--- a/spot/tl/formula.cc
+++ b/spot/tl/formula.cc
@@ -1632,10 +1632,10 @@ namespace spot
         break;
       case op::first_match:
         props = children[0]->props;
-        // If first_match(r) == r && !(r;[*]), then it should follow
-        // that if r is stutter-inv, then first_match(r) is
-        // stutter-inv, so we do not reset the syntactic_si bit.
         assert(is_.sere_formula);
+        // {(a[+];b*);c*}<>->d is stutter invariant
+        // {first_match(a[+];b*);c*}<>->d is NOT.
+        is_.syntactic_si = false;
         is_.boolean = false;
         is_.ltl_formula = false;
         is_.psl_formula = false;
diff --git a/tests/core/kind.test b/tests/core/kind.test
index e07fd02b9..db04fc6d2 100755
--- a/tests/core/kind.test
+++ b/tests/core/kind.test
@@ -136,6 +136,8 @@ Fa  M b,&!xLPgopra
 (!p W Gp) | ({(!p[*];(p[+]:(p[*];!p[+])))[:*4][:+]}<>-> (!p W Gp)),&!xPpla
 {b[+][:*0..3]},&!fPsopra
 {a->c[*]},xfPsopra
+{(a[+];b*);c*}<>->d,&!xfPgopra
+{first_match(a[+];b*);c*}<>->d,&!fPgopra
 EOF
 
 run 0 ../kind input