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In this paper we compute the group H 2(SL 2(F)), for F an infinite field. In particular, using some techniques from homological algebra developed by Hutchinson [Hutchinson, K: K-Theory 4 (1990), 181–200], we give a new proof of the following theorem obtained by [Su2]: The group H 2(SL 2, (F)) is the fiber product of λ*:K 2(F)→ I 2(F)/I 3(F) and σ: I 2(F) → I 2(F)/I 3(F) where λ* and σ map onto I 2(F)/I 3(F).