In 1994 R. Srivastava defined the concepts of basis and subbasis, for a smooth fuzzy topology, described a way to obtain a topology from a basis and also discussed the product spaces. We point out that a topology obtained from a basis or a subbasis given in that paper is not well defined. So we redefine the concept of basis and subbasis for a smooth fuzzy topology in a natural manner so that every smooth fuzzy topology becomes a basis as well as a subbasis of itself. We also define and discuss product of smooth fuzzy topological spaces using the new definition of basis introduced in this paper.