The two neuron CNN system with piecewise linear activation function and time dependent external inputs is analyzed and the parametric solutions for the trajectories are given. We look then at the particular case in which the CNN has an antisymmetric template and sine external input. For particular parameter values, this example has been found in the literature to have chaotic behavior. We use the trajectories solution to study the sensitivity of the system to initial conditions and the possibility of self-intersecting trajectories. Both results characterize a chance for a chaotic behavior.