Explicit results on solution, stability and reduction of a class of discrete-time linear time-varying systems are presented. It is shown that the state transition matrix can be computed explicitly by φ(k,0)=A1kA2k,whereA1andA2are constant matrices. The stability is completely determined by eigenvalues ofA1andA2. It is also shown that the system can be reduced to a time-invariant one by an algebraic transformation. Examples are given to show that stability criteria of linear time-invariant systems cannot, in general, be applied to time-varying cases.