Within the theory of spline functions, there is always great interest in divided differences, since they provide one possibility to define \(B\)- splines, i.e. splines with minimal support. In the paper under consideration, which is part of the author's doctoral thesis, a new type of generalization of the univariate divided differences to the multivariate case is given. The definition of the multivariate divided difference is done via a pointwise evaluation of a suitable function of \(s\) vector variables. Furthermore, several interesting properties of the multivariate divided differences are derived, a new generalization of truncated power functions is given, and a link with simplex splines is established.