A new Markovian model for burst-error processes is herein presented. Our basic idea consists of imposing a convenient structure on this model, with the double purpose of reproducing the generation of some typical patterns of burst error sequences and facilitating the maximum-likelihood estimation of the model's parameters. A simple procedure for calculating the maximum-likelihood metric of those parameters is derived and numerically maximized to fit the model to data. Some numerical results are presented that illustrate the effectiveness of this approach in reproducing very well important statistics of burst-errors processes.