It has been more than 40 years since the first studies of the secondary visual cortex (V2) were published. However, no concrete hypothesis on how the receptive field of V2 neurons supports general shape processing has been proposed to date. Using a computational model that follows the principle of self-organization, we advance two hypotheses in this letter: (1) typical V2 orientation-selective receptive field contains a primary orientation and a secondary orientation component, forming a corner, a junction, or a cross; and (2) V2 columns with the same primary orientation form contiguous domains, divided into subdomains that prefer different secondary orientations. The first hypothesis is consistent with existing experimental evidence, and both hypotheses can be tested with current techniques in animals. In this manner, computational modeling can be used to provide verifiable predictions that eventually allow us to understand the role of V2 in visual processing.