For the purist regardless is the only word to use when one refers to someone or something that has absolutely no regard for someone or something else. We say, “Regardless of your money, I will not be bought.” Or “Regardless of how busy you are, I expect you to be at my piano recital.” Irregardless is commonly accepted as meaning the same thing and is in most standard dictionaries today, but it is like a stepchild in the grammar family. Technically speaking irregardless is a double negative and should be avoided. Besides, Microsoft Word always puts a little green line under it in any writing you do.