We consider a speaker independent hidden Markov model (HMM) based isolated word speech recognition system. The most general representation of the probability density function (PDF), in the classical HMM, is a parametric one (i.e., a Gaussian). We derive an unsupervised, nonparametric and multidimensional Bayesian classifier based on the well known orthogonal probability density function (PDF) estimator which does not assume any knowledge of the distribution of the conditional PDFs of each class. Such a result is possible since this nonparametric estimator is suitable and adapted to the expectation maximization (EM) mixture identification algorithm