Abstract: Several methods for testing stability of first quadrant quarter-plane two dimensional (2-D) recursive digital filters have been suggested in 1970`s and 80`s. Though Jury`s row and column algorithms, row and column concatenation stability tests have been considered highly efficient they still fall short of accuracy if the computational time is a major consideration. In this research we present a very simple method which requires very little computation time particularly when applied to the second order 2-D filter.