Not directly, but if you have an intermediate version, you can do a two step conversion of the file. Here's a knowledgebase article on the subject: http://help.filemaker.com/app/answers/detail/a_id/750/kw/migration
Given that big a change in versions, you'll likely have to do additional fixes to the file after conversion is done.
Your other option is to export the data from the filemaker 4 file as text ( csv, tab or merge ) file and import the data into a brand new filemaker 11 file. This, of course, would require you to start over with your script and layout designs.