The authors use the classical Schur reduction procedure to give a lattice filter implementation of the Chandrasekhar recursions. The derivation is based on the observation that the covariance matrix of a process with a time-invariant state-space model is structured. This allows one to easily derive the connection between the Schur algorithm and spectral factorization and to extend the Chandrasekhar recursions to the case of nonsymmetric Riccati equations. The Chandrasekhar recursions can be implemented in scalar steps using a sequence of well-defined elementary (hyperbolic and Givens) rotations.