Many computational models have been proposed for interpreting the properties of neurons in the primary visual cortex (V1). But relatively fewer models have been proposed for interpreting the properties of neurons beyond VI. Recently, it was found that the sparse deep belief network (DBN) could reproduce some properties of the secondary visual cortex (V2) neurons when trained on natural images. In this paper, by investigating the key factors that contribute to the success of the sparse DBN, we propose a hierarchical model based on a simple algorithm, K-means, which can be realized by competitive Hebbian learning. The resulting model exhibits some response properties of V2 neurons, and it is more biologically feasible and computationally efficient than the sparse DBN. (C) 2014 Elsevier B.V. All rights reserved.