diff --git a/Lib/zipfile.py b/Lib/zipfile.py
index 9e96e93..46ec6ef 100644
--- a/Lib/zipfile.py
+++ b/Lib/zipfile.py
@@ -165,6 +165,7 @@
         return endrec
 
     # Update the original endrec using data from the ZIP64 record
+    endrec[_ECD_SIGNATURE] = sig
     endrec[_ECD_DISK_NUMBER] = disk_num
     endrec[_ECD_DISK_START] = disk_dir
     endrec[_ECD_ENTRIES_THIS_DISK] = dircount
@@ -733,9 +734,8 @@
 
         # "concat" is zero, unless zip was concatenated to another file
         concat = endrec[_ECD_LOCATION] - size_cd - offset_cd
-        if endrec[_ECD_LOCATION] > ZIP64_LIMIT:
-            # If the offset of the "End of Central Dir" record requires Zip64
-            # extension structures, account for them
+        if endrec[_ECD_SIGNATURE] == stringEndArchive64:
+            # If Zip64 extension structures are present, account for them
             concat -= (sizeEndCentDir64 + sizeEndCentDir64Locator)
 
         if self.debug > 2:
diff --git a/Misc/NEWS b/Misc/NEWS
index 8cc1af0..bc6ede7 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -86,6 +86,13 @@
 Library
 -------
 
+- Issue #3535: zipfile couldn't read some zip files larger than 2GB.
+
+- Issue #3776: Deprecate the bsddb package for removal in 3.0.
+
+- Issue #3762: platform.architecture() fails if python is lanched via
+  its symbolic link.
+
 - Issue #3660: fix a memory leak in the C accelerator of the pickle module.
 
 - Issue #3160: the "bdist_wininst" distutils command didn't work.