Abstract: Let φ₁, φ₂ be two refinable functions with the dilation factor a.A new method for constructing the refinable function based on the convolution of functions φ₁, φ₂ is presented.The properties such as periodicity and symmetry of the refinable function generated by the convolution of functioins φ₁, φ₂ are discussed.The B-spline function N_{i +j}(x) can be constracted by the convolution (N_i *N_j) (x) of two B-spline functions N_i(x) and N_j(x).Finally, two examples are given to illustrate how to use the method to construct refinable function.

Key words: refinable function, mask, convolution, scaling function