Using the generalized interval arithmetic we give a generalized cholesky decomposition. Generalized intervals (intervals whose bounds are not constrained to be increasingly ordered) extend classical intervals providing better algebraic properties. In particular, the generalized interval arithmetic is a group for addition and for multiplication of zero free intervals. These properties allow one constructing a cholesky decomposition of a generalized interval matrix A: the computed generalized interval matrix L satisfy A=LL^Twith equality instead of the weaker inclusion obtained in the context of classical intervals.