Abstract: This study aims a method of testing the Bounded Input Bounded Output (BIBO) stability of recursive 2-Dimensional (2-D) digital filters using the method for computation of variance or 2-D complex integrals. In the case when the non-essential singularities of the second kind (NSSK) are present, a method is given to determine whether the filter is l1 stable. The method seems to be very simple for lower order filters and even for higher order filters.