diff --git a/pygobject-3.38.0.tar.xz b/pygobject-3.38.0.tar.xz
deleted file mode 100644
index eb3c13f..0000000
--- a/pygobject-3.38.0.tar.xz
+++ /dev/null
@@ -1,3 +0,0 @@
-version https://git-lfs.github.com/spec/v1
-oid sha256:0372d1bb9122fc19f500a249b1f38c2bb67485000f5887497b4b205b3e7084d5
-size 553892
diff --git a/pygobject-3.40.0.tar.xz b/pygobject-3.40.0.tar.xz
new file mode 100644
index 0000000..9d6abd2
--- /dev/null
+++ b/pygobject-3.40.0.tar.xz
@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:67d61fac9f5aa83bf2edccbc286802ce0f1c3dde8f83103b7c765b91a6ed905f
+size 555920
diff --git a/python-gobject.changes b/python-gobject.changes
index 5545ac0..7de2eff 100644
--- a/python-gobject.changes
+++ b/python-gobject.changes
@@ -1,3 +1,12 @@
+-------------------------------------------------------------------
+Fri Mar 19 20:08:28 UTC 2021 - Michael Gorse <mgorse@suse.com>
+
+- Update to version 3.40.0:
+  + GTK 4 compatibility fixes.
+  + Python 3.9 and 3.10 compatibility fixes.
+  + New minimal dependency requirements.
+- Up glib2, gobject-introspection, and cairo required versions.
+
 -------------------------------------------------------------------
 Wed Jan 13 12:59:29 UTC 2021 - Benjamin Greiner <code@bnavigator.de>
 
diff --git a/python-gobject.spec b/python-gobject.spec
index d8dd9ed..c78e4ed 100644
--- a/python-gobject.spec
+++ b/python-gobject.spec
@@ -28,15 +28,15 @@
 %global __requires_exclude_from ^%{_libdir}/python.*/site-packages/gi/__init__.py$
 %define _name   pygobject
 Name:           python-gobject
-Version:        3.38.0
+Version:        3.40.0
 Release:        0
 Summary:        Python bindings for GObject
 License:        LGPL-2.1-or-later
 Group:          Development/Languages/Python
 URL:            https://wiki.gnome.org/Projects/PyGObject/
-Source0:        https://download.gnome.org/sources/pygobject/3.38/%{_name}-%{version}.tar.xz
+Source0:        https://download.gnome.org/sources/pygobject/3.40/%{_name}-%{version}.tar.xz
 
-BuildRequires:  %{python_module cairo >= 1.11.1}
+BuildRequires:  %{python_module cairo >= 1.16.0}
 BuildRequires:  %{python_module cairo-devel}
 BuildRequires:  %{python_module devel}
 BuildRequires:  %{python_module setuptools}
@@ -100,8 +100,8 @@ addon libraries such as pygtk.
 %package -n %{name}-common-devel
 Summary:        Shared development files for GObject's Python bindings
 Group:          Development/Languages/Python
-Requires:       glib2-devel >= 2.38.0
-Requires:       gobject-introspection-devel >= 1.46.0
+Requires:       glib2-devel >= 2.56.0
+Requires:       gobject-introspection-devel >= 1.56.0
 Requires:       libffi-devel >= 3.0.0
 Requires:       pkgconfig(cairo)
 Requires:       pkgconfig(cairo-gobject)
@@ -123,7 +123,6 @@ export CFLAGS="%{optflags}"
 %install
 %python_install
 
-
 %{python_expand # delete unwanted python scripts and their compiled cache files
 # Drop pygtkcompat layer - It's useless and we lack other stuff for it to work
 rm -v %{buildroot}%{$python_sitearch}/gi/pygtkcompat.py*
@@ -139,7 +138,6 @@ find %{buildroot} "(" -name '*.la' -or -name '*.a' ")" -delete
 %{?python_compileall}
 %python_expand %fdupes %{buildroot}%{$python_sitearch}
 
-
 %files %{python_files}
 %license COPYING
 %doc NEWS