You start flipping cards over one at a time and holding them in one hand. When you have two cards of the same suit that are separated by two other cards (e.g. 4♣ 2♦ 7♥ 10♣), you discard the middle two. When two cards of the same value are separated by two other cards (e.g. 4♣ 2♦ 7♥ 4♥), you discard all four.
This game is neither Accordion nor Royal Marriage, but bears similarities to both. Somebody else asked this same question on Yahoo Answers five years ago and the response was unsatisfactory.
If someone can identify this game, I would also like to know what happens when you finish with two cards left: do you win, as in Royal Marriage, or not?