In this paper, we study further a class of cellular neural networks model with delays. By employing the inequality api(m)(k=1)1 b(q(k))(k) <or= 1/r sigma(m)(k=1) q(k)b(r)(k) + 1/r a(r) (a >or=0, b(k) >or=0, q(k) > 0 with sigma(m)(k=1) q(k) = r-1, and r > 1), constructing a new Lyapunov functional, and applying the Homeomorphism theory, we derive some new conditions ensuring the existence, uniqueness of the equilibrium point and its global exponential stability for cellular neural networks. These conditions are independent of delays and possess infinitely adjustable real parameters, which are of highly important significance in the designs and applications of networks. In addition, we extend or improve the previously known results.