diff --git a/src/PIL/EpsImagePlugin.py b/src/PIL/EpsImagePlugin.py
index 380b1cf0ec4..f31b1c1a2d0 100644
--- a/src/PIL/EpsImagePlugin.py
+++ b/src/PIL/EpsImagePlugin.py
@@ -230,6 +230,11 @@ def _open(self) -> None:
         trailer_reached = False
 
         def check_required_header_comments() -> None:
+            """
+            The EPS specification requires that some headers exist.
+            This should be checked when the header comments formally end,
+            when image data starts, or when the file ends, whichever comes first.
+            """
             if "PS-Adobe" not in self.info:
                 msg = 'EPS header missing "%!PS-Adobe" comment'
                 raise SyntaxError(msg)
@@ -270,6 +275,8 @@ def _read_comment(s: str) -> bool:
             if byte == b"":
                 # if we didn't read a byte we must be at the end of the file
                 if bytes_read == 0:
+                    if reading_header_comments:
+                        check_required_header_comments()
                     break
             elif byte in b"\r\n":
                 # if we read a line ending character, ignore it and parse what
@@ -365,8 +372,6 @@ def _read_comment(s: str) -> bool:
                 trailer_reached = True
             bytes_read = 0
 
-        check_required_header_comments()
-
         if not self._size:
             msg = "cannot determine EPS bounding box"
             raise OSError(msg)