This paper presents an improved necessary and sufficient condition of exponential stability for LTI delay systems. By this criterion, the stability analysis of any system of the class can be reduced to verification of the positive definiteness of a special matrix (which is based on the delay Lyapunov matrix). The dimension of the matrix depends on the parameters of the system, and the goal of this paper is to make it smaller. We applied a new technique, and reduced the dimension by about half.