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The famous F5 algorithm for computing Gr(o)bner basis was presented by Faugère in 2002.The original version of F5 is given in programming codes,so it is a bit difficult to understand.In this paper,the F5 algorithm is simplified as F5B in a Buchberger’s style such that it is easy to understand and implement.In order to describe F5B,we introduce F5-reduction,which keeps the signature of labeled polynomials unchanged after reduction.The equivalence between F5 and F5B is also shown.At last,some versions of the F5 algorithm are illustrated.