A standard method for fitting the multinomial logit model, used in some statistical packages, is to represent it in terms of the equivalent Poisson log-linear model. The constraint necessary for this equivalence requires the inclusion of a set of nuisance parameters in the Poisson model, of dimension equal to the number of distinct values of the set of covariates. In such packages the model is therefore restricted to the analysis of categorical covariates, i.e. contingency tables. This paper describes a method for fitting the multinomial logit model which requires only a simple scoring algorithm, but does not use the equivalent Poisson model, and can be used with continuous covariates with an unlimited number of distinct values. The method is implemented as a set of GLIM macros. An example is discussed.