A procedure is presented for identifying the system triple {A, B, C} and the system order for linear, constant, multivariable, discrete-time plants from actual input-output data. The approach is based on the minimal realization and the cross-correlation technique between the input sequence and the output measurement sequence. The dimension of the system is determined from checking the rank of the Hankel matrix which is constructed by the Markov parameter estimates obtained by the auto-correlation of the input sequence and the cross-correlation between the input sequence and the output sequence. The estimates of the triple {A, B, C} are calculated by Markov parameter estimates using minimal realization algorithm.