The problem of designing modular linear systolic arrays for dynamic programming was raised in [9]. An attempt to solve this problem appeared in [8]. Unfortunately, the size of the local memory of each processor and the time delay between two consecutive processors of this array (in [8]) are still depending on n as in [9]. Moreover, these two arrays (in [8, 9]) are partially pipelined. Some elements have to be initially stored in the array. However, the difference between these two linear arrays is that the one in [8] is faster and more easy to handle than in [9]. In this paper we discuss a way of designing fully — pipelined modular linear systolic arrays for dynamic programming. The algorithm we obtain requires n2+1 processors (or simply cells) and 6n2-n-3 time steps for its execution: each cell has a local memory of size 1 and the time delay between two consecutive cells of the array is constant. As far as the author knows, It is the only fully-pipelined modular linear systolic array algorithm for dynamic programming appearing in the literature for the moment.