A multivariate modelling may involve a set of multivariate functions. A vector valued function structure can be used to mathematically express the given problem and each multivariate function can be considered as an element of this vector. This work aims to construct a new approach representing the elements of this vector structure in terms of less-variate functions to reduce the computational complexity. For this purpose, a new method based on the plain High Dimensional Model Representation (HDMR) philosophy is developed. The basic concepts of this method and several illustrative numerical implementations are given here.