I would like to create a template for site pages and use it on all subwebsites. A template is located on the topmost website in the standard library for pages. I get this template when I use the drop-down menu on the start page and want to create a new page. There are the three templates that are displayed by default and my own. This works on the website as usual, but this template should be usable on all subsites. I don't want to have them redundant in the sharepoint, that leads to errors and more effort if the template should be edited.
Can you think of a solution to this problem?