Digital filters with variable frequency responses are called variable digital filters. Generally speaking, variable recursive digital filters require lower orders and less computational complexity to satisfy the same desired variable magnitude responses than nonrecursive filters, but the stability of variable recursive filters is difficult to guarantee since their coefficients are also varied in some manner. This paper presents an improved version of an existing algorithm for designing variable recursive one-dimensional (1-D) digital filters with guaranteed stability, which is an improved version of the existing one. The basic idea is to find both the numerator and the denominator coefficients of the transfer function of a variable recursive filter as multi-dimensional (M-D) polynomials of the spectral parameters that define variable magnitude characteristics. To guarantee the stability, some stability constraints have to be imposed on the denominator coefficients. Therefore, we first substitute the denominator coefficients by another set of variables whose values can be arbitrary but without affecting the stability. Then both the numerator and the new denominator coefficients are determined as M-D polynomials of the spectral parameters. Compared to the existing design method, the new one is simpler, but does not degrade the final design accuracy. Two design examples are given to compare the new design method with the existing one.