Update creating a new record?

I've noticed that every time I "update" a record, mySQL is actually adding a new record (highest number ID, at the end) and deleting the original record. I don't understand this. For example, if I edit a phone number in the listing for ID=023, the next time I view a complete listing of members I'll see that person's link now showing ID=128 (or a similar much higher record number, 1 higher than the last highest record number). My PHP code uses "upate photographers" to update rather than insert a new record. I can post the actual code tonight if needed, but I was hoping that someone might have an idea of whether or not this was normal. It DOES pull up the right data after I update mySQL, but it's the change in the link that bites me on one other page with hard-coded links. Wm