This report deals with the problem of designing cellular neural networks (CNNs) for associative memories. Concerning the problem, a design method of sparsely connected neural networks by means of the singular value decomposition has been proposed, and we can design CNNs by using this method. However this method has a problem that the complete stability of a designed CNN is not guarateed because the CNN has non-symmetric connections in general. In this report, we give a new design method of CNNs which guarantees the symmetry of connections. Any CNN designed by our method is completely stable, because it has been proved that a CNN with symmetric connections is completely stable.