Given an observable system (C, A) is an element of K-nxn x K-nxn with K = R or C, the set of (C, A)-invariant subspaces having the restricted system fixed observability indices is a smooth manifold embedded on the corresponding Grassmannian. We obtain an explicit parametrization of it by means of an atlas of coordinate charts. This parametrization can be applied to solve some design problems related to the disturbance decoupling problem.