  This work is based on an earlier proposal \cite{hs} that the membrane B-F
theory consists of matter fields alongwith Chern-Simons fields as well as the
auxiliary pairs of scalar and tensor fields. We especially discuss the
supersymmetry aspects of such a membrane theory. It is concluded that the
theory possesses maximal supersymmetry and it is related to the L-BLG theory
via a field map. We obtain fuzzy-sphere solution and corresponding tensor field
configuration is given.
