Summary: A new class of continuous transformations defined on the Euclidean space \((\mathbb{R}^n \to \mathbb{R}^n)\) is applied to vectors of independent normally distributed random variables. The output of such a transformation is a random vector, such that its density turns out to be a generalization of the multivariate normal (called pseudonormal throughout this paper) with possible applications to model multicomponent system reliability. Each multivariate normal density is also pseudonormal as a special case. Some properties of both the class of transformations and the class of pseudonormals are investigated. Especially interesting is the fact that the class of pseudonormals is invariant with respect to the class of transformations. Furthermore the two classes can be regarded as isomorphic nonabelian groups.