The contraction mapping principle is used to obtain sufficient conditions for the bounded-input bounded-output (BIBO)stability of a class of single-loop discrete-data systems with a single continuous non-linearity in the feedback path. The boundedness of the output is considered only at the discrete instants of sampling. The method of obtaining the best bounds for the sampled input and output in a particular case of the non-linearity is discussed. A numerical example is given to illustrate the technique of analysis