Unstable zeros limit the achievable control performance. When a continuous-time system is discretized using the zero-order hold, there is no simple relation which shows how the zeros of the continuous-time system are transformed by sampling. This paper analyzes the asymptotic behavior of the limiting zeros for multivariable systems and derives a new condition for the zeros to be stable for sufficiently small sampling periods. Furthermore, the result is applied to a collocated matrix second-order system.