Directory name changes case when copied from USB to RedHat
I have a USB drive that I use to copy backup files from a RedHat system to a windows system and vice versa. My problem is that when I copy the directories from RH to the usb drive, the case changes from upper case to lower case. It's not that way for ALL directories, and it doesn't do that for any files. I don't want to change the format of the USB drive to ext3 because then I can't use it for my Windows systems (right?).
Is there any other way to keep it from changing my file names? A script or anything is fine.