You can upgrade from 4.1 to FileMaker 11. You can download the 30 day free trial for Filemaker 11 and see what happens when you attempt to convert your files.
Before doing so, you will want to read this knowledge base artical: http://help.filemaker.com/app/answers/detail/a_id/750/kw/converting
Please be prepared for the fact that you will not be able to simply convert your files and start using them. FileMaker has undergone considerable changes from 4.1 to 11. If you have a fairly simple system of just a few files, they may convert cleanly and require only a small number of adjustments. If you have large numbers of files with many complex relationships and scripts, it may take quite a bit more effort to modify the converted files until they work for you. You may even find that exporting the data from your converted files into a brand new version 11 database you have created from "the ground up" makes more sense.
You may also find thes tools may offer more assistance when getting your converted files up and running:
FileMaker Advanced--database design reports and script debugger can save a lot of time.
FMMigrator--haven't used it myself, but I understand it can be used to help merge the separate files into a single unified file.
FMDIff--can help check your files for possible file corruption.
Thanks so kindly PhilModJunk, for your help response to my question regarding upgrading 4.1 FM Pro to 64bit operating system. I believe I will have to make the jump. Any thoughts on FM Pro 10.0 for this purpose? I believe I heard someone say once that you could use it on both systems??? Not sure. However, it is still possible to get that version if would make conversion simpler... thanks kindly.
The upgrade process from 4.1 to 10 and 4.1 to 11 would be virtually identical so I would go for the most recent release to take advantage of the latest features in FileMaker.