diff --git a/cmake/FindPROJECT_NAME.cmake.in.in b/cmake/PROJECT_NAMEConfig.cmake.in.in
similarity index 100%
rename from cmake/FindPROJECT_NAME.cmake.in.in
rename to cmake/PROJECT_NAMEConfig.cmake.in.in
diff --git a/cmake/create_cmake_config_files.cmake b/cmake/create_cmake_config_files.cmake
index deda9ac6342635380eae2ff01f65e247840cc57c..3f02fa46d1aa1235ff2d2a4663029d2b18f6e1c6 100644
--- a/cmake/create_cmake_config_files.cmake
+++ b/cmake/create_cmake_config_files.cmake
@@ -53,17 +53,22 @@ endforeach()
 
 # we have nested @-statements, so we have to parse twice:
 
-# create the cmake Find package script
-configure_file(cmake/FindPROJECT_NAME.cmake.in.in "${PROJECT_BINARY_DIR}/cmake/Find${PROJECT_NAME}.cmake.in" @ONLY)
-configure_file(${PROJECT_BINARY_DIR}/cmake/Find${PROJECT_NAME}.cmake.in "${PROJECT_BINARY_DIR}/Find${PROJECT_NAME}.cmake" @ONLY)
+# create the cmake find_package configuration file
+configure_file(cmake/PROJECT_NAMEConfig.cmake.in.in "${PROJECT_BINARY_DIR}/cmake/${PROJECT_NAME}Config.cmake.in" @ONLY)
+configure_file(${PROJECT_BINARY_DIR}/cmake/${PROJECT_NAME}Config.cmake.in "${PROJECT_BINARY_DIR}/${PROJECT_NAME}Config.cmake" @ONLY)
 
 # create the shell script for standard make files
 configure_file(cmake/PROJECT_NAME-config.in.in "${PROJECT_BINARY_DIR}/cmake/${PROJECT_NAME}-config.in" @ONLY)
 configure_file(${PROJECT_BINARY_DIR}/cmake/${PROJECT_NAME}-config.in "${PROJECT_BINARY_DIR}/${PROJECT_NAME}-config" @ONLY)
 
-# install the script
-install(FILES "${PROJECT_BINARY_DIR}/Find${PROJECT_NAME}.cmake"
-  DESTINATION share/cmake-${CMAKE_MAJOR_VERSION}.${CMAKE_MINOR_VERSION}/Modules COMPONENT dev)
+# install cmake find_package configuration file
+install(FILES "${PROJECT_BINARY_DIR}/${PROJECT_NAME}Config.cmake"
+  DESTINATION lib/cmake/${PROJECT_NAME} COMPONENT dev)
 
+# install same cmake configuration file another time into the Modules cmake subdirectory for compatibility reasons
+install(FILES "${PROJECT_BINARY_DIR}/${PROJECT_NAME}Config.cmake"
+  DESTINATION share/cmake-${CMAKE_MAJOR_VERSION}.${CMAKE_MINOR_VERSION}/Modules RENAME Find${PROJECT_NAME}.cmake COMPONENT dev)
+
+# install script for Makefiles
 install(PROGRAMS ${CMAKE_CURRENT_BINARY_DIR}/${PROJECT_NAME}-config DESTINATION bin COMPONENT dev)