Let's just be clear which flag we are talking about! Like Dave Mckenzie, i was taught (in the Guides, not Scouts!) that St Patrick's flag was a red DIAGONAL cross on a white background, and as he says, forms that part of the Union flag.
However, my Northern Irish brother-in-law insisted that i was wrong, and that it was a red horizontal/vertical cross on a white background (like St George's flag) with hand in the middle: is that not the Ulster flag? See: http://en.wikipedia.org/wiki/Northern_Ireland_flags_issue