A multiplicative function f is said to be specially multiplicative if there is a completely multiplicative function f A such that f ( m ) f ( n ) = ∑ d | ( m , n ) f ( m n / d 2 ) f A ( d ) for all m and n . For example, the divisor functions and Ramanujan's τ -function are specially multiplicative functions. Some characterizations of specially multiplicative functions are given in the literature. In this paper, we provide some further characterizations of specially multiplicative functions.