This paper proposes a new design method for a class of FIR low-pass filters characterized by steep cut-off in the frequency domain and having a small number of taps. Although existing methods such as the Remez method can realize an FIR filters with a small number of taps by simply cascading scaled filters, the resulting characteristics can be such that their cut-off edges are not steep. Our proposed method significantly improves this shortcoming by employing certain frequency scalings of the basis filters that make up the cascaded structure. It turns out that the scaling function can be written as recursion of the basis filter and is referred to as the mean operation. The mean operation is performed in such a way that the boundaries of the transition region are narrowed by recursive subtraction so that the gradient of transition is increased, resulting in a steep characteristics. Experimental results show that the proposed method approximate the desired characteristics with smaller number of taps when compared with conventional methods.