The paper considers a Gaussian-integer preserving (GIP) form for the author's method to test whether a polynomial with complex coefficients has its zeros inside the unit-circle (is 'stable'). The GIP property describes the fact that for a polynomial with Gaussian integer (i.e. "complex integer") coefficients, the test is carried out completely over Gaussian integers. The proposed algorithm has linear growth of the size of coefficients and an implied low binary complexity. This property is advantageous for deriving simpler stability constraints on designable parameters. It can also be exploited to reduce obstruction of decision about stability that can be introduced by numerical inaccuracy when testing ill-conditioned or high degree polynomials.