Markov random field (MRF) is commonly used in modelling spatially dependent data. These models are often referred to as auto-models. While univariate auto-models have been extensively studied in the literature, discrete multivariate MRF has not attracted much attention. This paper attempts to fill the research gap by providing some results on the discrete multivariate MRF scheme, which forms the theoretical foundation to construct models for spatially dependent categorical data. The results presented in this paper allow the formulation of a novel auto-model and justify the validity of the recently proposed auto-multinomial model.