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We show that any N×M-dimensional delayed cellular neural network described using cloning templates can have no more than 3N×M isolated equilibrium points and 2N×M of these equilibrium points located in saturation regions are locally exponentially stable. In addition, we give the conditions for the equilibrium points to be locally exponentially stable when the equilibrium points locate the designated saturation region. These conditions improve and extend the existing stability results in the literature. The conditions are also very easy to be verified and can be checked by direct examination of the templates, regardless of the number of cells. Finally, the validity and performance of the results are illustrated by use of two numerical examples.