Two delta-operator-based stability : tests, or more generally zero location tests. were recently proposed in a separate paper. Those tests establish two families of such tests, each spanning from the discrete-time to the continuous-time with the delta operator providing smooth transitions between the two domains. In this paper a third family is proposed. Specifically, the normalized Schur-Cohn test in the discrete-time domain is transformed into the delta-operator domain resulting in a new delta-operator test. The limit of this new test as the sampling interval vanishes is shown to be the recent Pham-Le Breton test in the continuous-time domain. Its relationships with the well-known Routh test and others are studied. A numerical example shows the advantage of the new test for fast sampling.