  The famous F5 algorithm for computing \gr basis was presented by Faug\`ere 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.
