We study global dynamical behavior of cellular neural networks (CNNs) consisting of two cells. Since the output characteristic of each cell is expressed by a piecewise-linear function, a CNN with two cells is considered as a planar piecewise-linear dynamical system. We present the necessary and sufficient condition for such a CNN to be completely stable under the assumptions that: 1) self-coupling coefficients take the same value greater than one and 2) biases are set to zero. The condition is explicitly expressed in terms of coupling coefficients between cells.