diff --git a/src/PIL/Image.py b/src/PIL/Image.py
index 272cf7b7b..1adca9ad5 100644
--- a/src/PIL/Image.py
+++ b/src/PIL/Image.py
@@ -3751,6 +3751,7 @@ class Exif(MutableMapping):
             self.endian = self._info._endian
         if offset is None:
             offset = self._info.next
+        self.fp.tell()
         self.fp.seek(offset)
         self._info.load(self.fp)