Fixed systems are limited in their performances to achieve the more complicated and higher level operations. Accordingly adaptive system, which adjusts itself in accorance with the time-varying environments, has been introduced to camouflarge the defficiency of fixed systems in varying environment, and adaptive filter is the outstanding fields in adaptive system. Adaptive recursive filter is far more efficient in that it can perform the signal processing with relatively lower filter order, but there remains severe problem in stability(convergency). On the basis of hyperstability introduced by V.M. Popov, a hyperstable new adaptive recursive filter is introduced which is theoretically guaranteed in stability. In this paper a more stable algorithm for adaptive recursive filter is devised