diff --git a/spacy/matcher/matcher.pxd b/spacy/matcher/matcher.pxd
index a146cd107..dd04153bf 100644
--- a/spacy/matcher/matcher.pxd
+++ b/spacy/matcher/matcher.pxd
@@ -17,6 +17,7 @@ cdef enum action_t:
     RETRY_ADVANCE = 0110
     MATCH_EXTEND = 1001
     MATCH_REJECT = 2000
+    MATCH_DOUBLE = 3000
 
 
 cdef enum quantifier_t:
diff --git a/spacy/matcher/matcher.pyx b/spacy/matcher/matcher.pyx
index f22b23260..260e72e40 100644
--- a/spacy/matcher/matcher.pyx
+++ b/spacy/matcher/matcher.pyx
@@ -332,6 +332,16 @@ cdef void transition_states(vector[PatternStateC]& states, vector[MatchC]& match
                 matches.push_back(
                     MatchC(pattern_id=ent_id, start=state.start,
                             length=state.length+1))
+            elif action == MATCH_DOUBLE:
+                # push match without last token if length > 0
+                if state.length > 0:
+                    matches.push_back(
+                        MatchC(pattern_id=ent_id, start=state.start,
+                                length=state.length))
+                # push match with last token
+                matches.push_back(
+                    MatchC(pattern_id=ent_id, start=state.start,
+                            length=state.length+1))
             elif action == MATCH_REJECT:
                 matches.push_back(
                     MatchC(pattern_id=ent_id, start=state.start,
@@ -439,6 +449,7 @@ cdef action_t get_action(PatternStateC state,
     RETRY_ADVANCE = 0110
     RETRY_EXTEND = 0011
     MATCH_REJECT = 2000 # Match, but don't include last token
+    MATCH_DOUBLE = 3000 # Match both with and without last token
 
     Problem: If a quantifier is matching, we're adding a lot of open partials
     """
@@ -476,8 +487,10 @@ cdef action_t get_action(PatternStateC state,
           return RETRY
     elif quantifier == ZERO_ONE:
       if is_match and is_final:
-          # Yes, final: 1000
-          return MATCH
+          # Yes, final: 3000
+          # To cater for a pattern ending in "?", we need to add
+          # a match both with and without the last token
+          return MATCH_DOUBLE
       elif is_match and not is_final:
           # Yes, non-final: 0110
           # We need both branches here, consider a pair like:
diff --git a/spacy/tests/regression/test_issue4120.py b/spacy/tests/regression/test_issue4120.py
index 652825064..4806d1607 100644
--- a/spacy/tests/regression/test_issue4120.py
+++ b/spacy/tests/regression/test_issue4120.py
@@ -6,15 +6,15 @@ from spacy.matcher import Matcher
 from spacy.tokens import Doc
 
 
-@pytest.mark.xfail
 def test_issue4120(en_vocab):
     """Test that matches without a final {OP: ?} token are returned."""
     matcher = Matcher(en_vocab)
     matcher.add("TEST", None, [{"ORTH": "a"}, {"OP": "?"}])
     doc1 = Doc(en_vocab, words=["a"])
     assert len(matcher(doc1)) == 1  # works
+
     doc2 = Doc(en_vocab, words=["a", "b", "c"])
-    assert len(matcher(doc2)) == 2  # doesn't work
+    assert len(matcher(doc2)) == 2  # fixed
 
     matcher = Matcher(en_vocab)
     matcher.add("TEST", None, [{"ORTH": "a"}, {"OP": "?"}, {"ORTH": "b"}])
@@ -24,4 +24,4 @@ def test_issue4120(en_vocab):
     matcher = Matcher(en_vocab)
     matcher.add("TEST", None, [{"ORTH": "a"}, {"OP": "?"}, {"ORTH": "b", "OP": "?"}])
     doc4 = Doc(en_vocab, words=["a", "b", "b", "c"])
-    assert len(matcher(doc4)) == 3  # doesn't work
+    assert len(matcher(doc4)) == 3  # fixed