This paper addresses the problem of computing fixed interval smoothed state estimates of a linear time varying Gaussian stochastic system. There already exist many algorithms that perform this computation, but all of them impose certain restrictions on system matrices in order for them to be applicable. This paper develops a new forwards--backwards pass algorithm that is applicable under the mildest restrictions possible - namely that the smoothed state distribtions exists in forms that can be characterised by means and covariances, for which this paper also develops a new necessary and sufficient condition.