Model management is essential for coping with the complexity introduced by the increasing number and varied nature of artifacts involved in MDE-based projects. Global Model Management (GMM) addresses this issue enabling the representation of artifacts, particularly transformation composition and execution, by a model called a megamodel. Typing information about artifacts can be used for preventing type errors during execution. In this work, we present a type system for GMM that improves its current typing approach and enables formal reasoning about the type of artifacts within a megamodel. This type system is able to capture non-trivial situations such as the use of higher order transformations.