Simplified forms of criteria are presented for ensuring that all zeros of a discrete system are stable when a continuous-time and strictly proper plant is discretised by the use of a sampler and a zero-order holder. The Nyquist algorithm proposed by Fu and Dumont has been improved in the sense that a point of the Nyquist curve is obtained analytically. When a lowpass system is sampled, analytical forms of criteria without drawing the Nyquist curves have been also shown.