By assembling the transition matrix of a finite discrete Markov chain from overlays of matrices which are defined only by the serial correlation coefficients and marginal distribution of the chain to be modelled, a considerable saving is made in the number of parameters required to define a multilag Markov chain. This parsimony is achieved without detriment to the marginal distribution or serial correlation structure of the modelled chain. Applications to daily precipitation sequences and reservoir reliability are outlined to demonstrate the model's versatility.
