The problem of classification in situations where the assumption of normality in the data is violated, and there are non-linear clustered structures in the dataset is addressed. A robust nonparametric kernel discriminant classification function, which is able to address this challenge, has been developed and the misclassification rates computed for various bandwidth matrices. A comparison with existing parametric classification functions such as the linear discriminant and quadratic discriminant is conducted to evaluate the performance of this classification function using simulated datasets. The results presented in this paper show good performance in terms of misclassification rates for the kernel discriminant classifier when the correct bandwidth is selected as compared to other identified existing classifiers. In this regard, the study recommends the use of the proposed kernel discriminant classification rule when one wishes to classify units into one of several categories or population groups where parametric classifiers might not be applicable.