Is it possible to re-train my cat?

My husband and I have had this cat for a year and a half. From the very beginning, he was litter-box trained, and relatively well behaved. We had him neutered around a year ago, and nothing really changed. However, in the last six weeks, he has developed the most annoying and disgusting habit. He relieves himself, not in the litter-box, but on the kitchen table! The horror! When he started doing this, nothing had changed in our routine. Since then, I’ve tried different brands of kitty litter, fancy-smelling litter-box fresheners for the litter-box, and I’ve cleaned the table a dozen times, with a variety of cleaners (including bleach and furniture polish). I put a tablecloth on it, but to no avail. Thus, I appeal to the collective. Is there away to save this situation? Or if not, is anyone on the market for a lovely cat?