A puzzle

A colleague (who is unreasonably organised) has organised our office secret santa today. Now nothing unusual about that but due to lots of cheating (ie it becoming known who is buying a present for whom) he has devised a system such that

1.  No one (including him) knows who is buying a present for who
2.  There is no chance of anyone being given themselves to buy a present for.

How has he done it?

(a clue – he has used sealed envelopes and labelled the envelopes)

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