Categorical data sequences occur in many applications such as forecasting, data mining and bioinformatics. In this note, we present higher-order Markov chain models for modelling categorical data sequences with an efficient algorithm for solving the model parameters. The algorithm can be implemented easily in a Microsoft EXCEL worksheet. We give a detailed description for the implementation which is accessible and useful to anyone who is interested in the applications of higher-order Markov chain models and has some knowledge of EXCEL.