An exact solution of the state differential quations for a power electronic circuit, incorporating a time discretization and a Basis Transformation, is presented. An eigen value -eigen vector expansion of the system matrix allows for the efficient evaluation of the State Transition matrix and Particular Integral. A binary search algorithm, without requiring the recalculation of the exponential matrix, can be used to obtain the state switching times. The Basis Transformation results in an exact solution when the input forcing function has an arbitrary time variation. Examples that illustrate the features of the method are presented.to the conventional Discrete Time Domain modelling method. The result can be termed the Modified Discrete Time Domain method. As a result of these modifications, the discrete time approach becomes very general as well as being computationally efficient. The closed form derivation of the new algorithm is presented and a comparison with the existing analytical models is provided. The efficiency of the improved algorithm is illustrated by several examples. Finally a step by step procedure of the improved discrete algorithm is outlined for transient, direct steady state or small signal analysis of power electronic circuits and systems.