When solving a stiff differential system by an implicit method, factorizing the Jacobian and solving the resulting linear equations often dominate the cost. We develop some methods related to a block Schur factorization of the Jacobian for separating the stiff components. These methods use block versions of the OR or LR algorithm or, for sparse Jacobians, orthogonal iteration to derive an approximate Jacobian. The technique is practical only for systems with relatively few stiff components.