diff --git a/binutils.spec b/binutils.spec
index ebe2225..f06db4f 100644
--- a/binutils.spec
+++ b/binutils.spec
@@ -2,7 +2,7 @@
 Summary: A GNU collection of binary utilities
 Name: binutils%{?_with_debug:-debug}
 Version: 2.35.2
-Release: 36%{?dist}
+Release: 37%{?dist}
 License: GPLv3+
 URL: https://sourceware.org/binutils
 
@@ -1177,18 +1177,22 @@ exit 0
 %if %{with crossbuilds}
 %if "%{_target_platform}" != "aarch64-redhat-linux"
 %exclude /usr/aarch64-redhat-linux/*
+%exclude /usr/bin/aarch64-redhat-linux-*
 %endif
 
 %if "%{_target_platform}" != "ppc64le-redhat-linux"
 %exclude /usr/ppc64le-redhat-linux/*
+%exclude /usr/bin/ppc64le-redhat-linux-*
 %endif
 
 %if "%{_target_platform}" != "s390x-redhat-linux"
 %exclude /usr/s390x-redhat-linux/*
+%exclude /usr/bin/s390x-redhat-linux-*
 %endif
 
 %if "%{_target_platform}" != "x86_64-redhat-linux"
 %exclude /usr/x86_64-redhat-linux/*
+%exclude /usr/bin/x86_64-redhat-linux-*
 %endif
 %endif
 
@@ -1260,6 +1264,9 @@ exit 0
 
 #----------------------------------------------------------------------------
 %changelog
+* Fri Jan 20 2023 Nick Clifton  <nickc@redhat.com> - 2.35.2-37
+- Stop the cross binaries from leaking into the native packages.
+
 * Thu Jan 19 2023 Nick Clifton  <nickc@redhat.com> - 2.35.2-36
 - Ensure that x76_64 and i686 versions of bfd_stdint.h are the same.  (#2162328)