diff --git a/ofxtools/header.py b/ofxtools/header.py
index 166713f..38a7127 100644
--- a/ofxtools/header.py
+++ b/ofxtools/header.py
@@ -273,7 +273,8 @@ def parse_header(source: BinaryIO) -> Tuple[OFXHeaderType, str]:
 
         # OFX header is read by nice clean machines, not meatbags -
         # should not contain 💩, 漢字, or what have you.
-        line = source.readline().decode("ascii")
+        # However, the first line may contain  the XML body, which CAN contain non-ascii.
+        line = source.readline().decode("ascii", "replace")
         if line.strip():
             found_header = True
             break
diff --git a/tests/test_header.py b/tests/test_header.py
index a1dfce6..3de6f1a 100644
--- a/tests/test_header.py
+++ b/tests/test_header.py
@@ -474,6 +474,16 @@ def testParseHeaderV2NoNewlineBetweenHeaderAndBody(self):
         self.assertIsNone(root.text)
         self.assertEqual(len(root), 1)
 
+    def testParseHeaderV2NoNewlineBetweenHeaderAndBodyWithUnicode(self):
+        """OFXv2 may contain non-ascii characters in the first line,
+        if the header is not separated from the body by newlines."""
+        ofxtools.header.parse_header(BytesIO(
+            b'<?xml version="1.0" encoding="utf-8" ?>'
+            b'<?OFX OFXHEADER="200" VERSION="202" SECURITY="NONE" OLDFILEUID="NONE" NEWFILEUID="NONE" ?>'
+            b'Dummy unicode data: A:\xc3\x83\xe2\x80\x9e\xc3\x83\xc2\xa4, '
+            b'O:\xc3\x83\xe2\x80\x93\xc3\x83\xc2\xb6, U:\xc3\x83\xc5\x93\xc3\x83\xc2\xbc, and SZ:\xc3\x83\xc5\xb8'
+        ))
+
     def testParseInvalid(self):
         header = str(self.headerClass(self.defaultVersion))
         with self.assertRaises(ofxtools.header.OFXHeaderError):