The problem of output feedback slidingmode control for sampled-data systems in the presence of external disturbances is considered. The proposed output feedback control strategy helps obtain a quasi slidingmode with an O(T-3) boundary layer, where T is the sampling period. This outperforms the O(T-2) result induced by the one-step delayed disturbance approximation method. The proposed scheme is applicable to linear systems which are relative degree one and minimum phase. An example is given to illustrate the efficacy of the new method.