transferring pics to computer - file names

ok so i've just got a new Nikon D60 which i LOVE. my only problem with it though is that it keeps resetting the file names. for example, it labels the first picture i take DSC_0001 and then the next one DSC_0002 and so on and so on, but once i copy those pictures onto my computer and delete them from my camera, the file names start over! so the next first pic i take is DSC_0001 and so on and so on. am i making sense? why does it do this? i didn't have this problem with my last camera, the file names simply continued on from where they left off. is it a problem with the camera or my computer? its just annoying, especially when i want to put a bunch of pictures in one place and i get all these "you already have a file named DSCwhatever, do you want to replace it?" warnings pop up. does anyone know how i can fix this? :confused:

On my Nikon D80 you can go into the SETUP MENU and turn ON the file no. sequence and it will give you continuous numbers up to 10,000 then it will reset and start over. With it off it resets each time you clear your cards, Jeff

thanks!! :thumbsup: