diff --git a/ffmpeg.spec b/ffmpeg.spec
index 46da505..e4ceace 100644
--- a/ffmpeg.spec
+++ b/ffmpeg.spec
@@ -36,6 +36,14 @@
 %bcond_with omxil
 %else
 
+# Use bundled openh264 headers on older Fedora/RHEL where the noopenh264 stub
+# package is not available
+%if 0%{?fedora} && 0%{?fedora} <= 39 || 0%{?rhel} && 0%{?rhel} <= 9
+%bcond_without bundled_openh264_headers
+%else
+%bcond_with bundled_openh264_headers
+%endif
+
 # Disable some features because RHEL 9 packages are too old
 %if 0%{?rhel} && 0%{?rhel} <= 9
 %bcond_with flite
@@ -92,7 +100,7 @@ Name:           ffmpeg
 %global pkg_name %{name}%{?pkg_suffix}
 
 Version:        6.1.1
-Release:        11%{?dist}
+Release:        12%{?dist}
 Summary:        A complete solution to record, convert and stream audio and video
 License:        GPL-3.0-or-later
 URL:            https://ffmpeg.org/
@@ -219,6 +227,9 @@ BuildRequires:  pkgconfig(ogg)
 BuildRequires:  pkgconfig(openal)
 BuildRequires:  pkgconfig(opencore-amrnb)
 BuildRequires:  pkgconfig(OpenCL)
+%if %{without bundled_openh264_headers}
+BuildRequires:  pkgconfig(openh264)
+%endif
 BuildRequires:  pkgconfig(opus)
 BuildRequires:  pkgconfig(rav1e)
 BuildRequires:  pkgconfig(rubberband)
@@ -550,7 +561,7 @@ This subpackage contains the headers for FFmpeg libswscale.
 %{gpgverify} --keyring='%{SOURCE3}' --signature='%{SOURCE2}' --data='%{SOURCE0}'
 %endif
 
-%autosetup -a1 -S git_am
+%autosetup %{?with_bundled_openh264_headers:-a1} -S git_am
 install -m 0644 %{SOURCE20} enable_decoders
 install -m 0644 %{SOURCE21} enable_encoders
 # fix -O3 -g in host_cflags
@@ -865,6 +876,9 @@ rm -rf %{buildroot}%{_datadir}/%{name}/examples
 %{_mandir}/man3/libswscale.3*
 
 %changelog
+* Tue Apr 23 2024 Kalev Lember <klember@redhat.com> - 6.1.1-12
+- Stop using bundled openh264 headers in F40+ and build against noopenh264
+
 * Wed Mar 13 2024 Sérgio Basto <sergio@serjux.com> - 6.1.1-11
 - Rebuild for jpegxl (libjxl) 0.10.2