Echoing what AcuraMechanic said; make sure you get a "Memory 1" remote as there is a difference. Also be sure to match the FCC ID number (should be E4EG8D-443H-A for an '01 CL).

I found the instructions to synch the remote somewhere on-line, but can't remember exactly where. It is in the official factory repair manual from HELM Corp. It is about a 12 or 13 step process and is fairly simple, but tedious. Just follow the instructions and it should work no problem. I was missing Memory 2 remote and bought a replacement one on ebay and everything worked out just fine.

BTW, where can you get a new one for only $35? My dealer wanted like $80 or so (IIRC); my recollection was that the new one cost like at least 3 times what the used one did. If you have trouble once you get it, I'll be glad to post the instructions from the HELM manual (although I don't check this site every day...). Good luck!