Beads carry over?

[MirkoEtDaimon]

Hi, I'm on my first playthrough and I've collected several beads, but not all. I see I can not collect them all, cause the first one is in a level you can't return to during the game/level selection.
I know that if you collect all the beads, you gain a sword you can use on the following games.
What I'd like to know is: if you don't get all the beads, still do the ones you've taken reamin during the following games?
Thanks, I'd like to know because if the answer is "yes", I'll do a little backtracking, otherwise I won't loose my time on that

EDIT: ok, I've done it. Even if you don' get all the beads during your first run ,still you keep the ones you've collected for the following game. Pheeeeew!