diff --git a/spacy/tests/doc/test_span.py b/spacy/tests/doc/test_span.py
index fcad4bf55..17997279d 100644
--- a/spacy/tests/doc/test_span.py
+++ b/spacy/tests/doc/test_span.py
@@ -1,4 +1,6 @@
 import pytest
+import numpy
+from numpy.testing import assert_array_equal
 from spacy.attrs import ORTH, LENGTH
 from spacy.tokens import Doc, Span, Token
 from spacy.vocab import Vocab
@@ -120,6 +122,17 @@ def test_spans_lca_matrix(en_tokenizer):
     assert lca[1, 0] == 1  # slept & dog -> slept
     assert lca[1, 1] == 1  # slept & slept -> slept
 
+    # example from Span API docs
+    tokens = en_tokenizer("I like New York in Autumn")
+    doc = Doc(
+        tokens.vocab,
+        words=[t.text for t in tokens],
+        heads=[1, 1, 3, 1, 3, 4],
+        deps=["dep"] * len(tokens),
+    )
+    lca = doc[1:4].get_lca_matrix()
+    assert_array_equal(lca, numpy.asarray([[0, 0, 0], [0, 1, 2], [0, 2, 2]]))
+
 
 def test_span_similarity_match():
     doc = Doc(Vocab(), words=["a", "b", "a", "b"])
diff --git a/spacy/tokens/doc.pyx b/spacy/tokens/doc.pyx
index 4858ad9dd..4ab8562c3 100644
--- a/spacy/tokens/doc.pyx
+++ b/spacy/tokens/doc.pyx
@@ -1673,7 +1673,7 @@ cdef int [:,:] _get_lca_matrix(Doc doc, int start, int end):
         j_idx_in_sent = start + j - sent_start
         n_missing_tokens_in_sent = len(sent) - j_idx_in_sent
         # make sure we do not go past `end`, in cases where `end` < sent.end
-        max_range = min(j + n_missing_tokens_in_sent, end)
+        max_range = min(j + n_missing_tokens_in_sent, end - start)
         for k in range(j + 1, max_range):
             lca = _get_tokens_lca(token_j, doc[start + k])
             # if lca is outside of span, we set it to -1