Abstract: In this paper we try to identify the funciton whose polynomial multiples are weak^* dense in thc BMOA space. Wc obtain that if|f(z)| ≥ |g(z)|at all points and if g is cyclic, then f is cyclic, Theorem 2 gives a sufficient and nccessary condition for a function to be cyclic is that f is an outer function.

Key words: Cyclic vectors, BMOA space, Outer function