diff --git a/spacy/errors.py b/spacy/errors.py
index 6e7ec49ae..61ff5a037 100644
--- a/spacy/errors.py
+++ b/spacy/errors.py
@@ -556,6 +556,8 @@ class Errors(object):
     E979 = ("Cannot convert {type} to an Example object.")
     E980 = ("Each link annotation should refer to a dictionary with at most one "
             "identifier mapping to 1.0, and all others to 0.0.")
+    E981 = ("The offsets of the annotations for 'links' could not be aligned "
+            "to token boundaries.")
     E982 = ("The 'ent_iob' attribute of a Token should be an integer indexing "
             "into {values}, but found {value}.")
     E983 = ("Invalid key for '{dict}': {key}. Available keys: "
diff --git a/spacy/gold/example.pyx b/spacy/gold/example.pyx
index 841b233c4..2ecee1821 100644
--- a/spacy/gold/example.pyx
+++ b/spacy/gold/example.pyx
@@ -396,6 +396,8 @@ def _parse_links(vocab, words, spaces, links):
             start_char, end_char = index
             start_token = starts.get(start_char)
             end_token = ends.get(end_char)
+            if start_token is None or end_token is None:
+                raise ValueError(Errors.E981)
             for i in range(start_token, end_token+1):
                 ent_kb_ids[i] = true_kb_ids[0]
 
diff --git a/spacy/tests/test_new_example.py b/spacy/tests/test_new_example.py
index b89654554..58eab4a54 100644
--- a/spacy/tests/test_new_example.py
+++ b/spacy/tests/test_new_example.py
@@ -230,8 +230,7 @@ def test_Example_from_dict_with_links(annots):
     [
         {
             "words": ["I", "like", "New", "York", "and", "Berlin", "."],
-            "entities": [(7, 15, "LOC"), (20, 26, "LOC")],
-            "links": {(0, 1): {"Q7381115": 1.0, "Q2146908": 0.0}},
+            "links": {(7, 14): {"Q7381115": 1.0, "Q2146908": 0.0}},
         }
     ],
 )