Neural processing of signals for object recognition and target search has been shown to implement an "untangling" transformation, whereby initial population representations are converted into a format that is linearly separable. Despite the appeal of this description, understanding the precise nature of these computations has proven difficult. Here we propose that a transformation analogous to the well-known Energy model for V1 complex cells can explain the untangling of target-match signals flowing from IT to Perirhinal cortex, collected as monkeys performed a delayed-match-to-sample task. For any N-way classification problem, "untangling" amounts to increasing the separation between the class means of the population response. For the IT to Perirhinal transformation, we hypothesized that untangling is achieved by transforming variance differences into mean differences through the use of a squaring operation. We optimized a linear-nonlinear-linear (LNL) response model to achieve this goal. The first linear stage transforms a population of IT inputs to maximize the variance differences between the classes in the output population. These linear responses are squared, and followed by a final orthogonal linear transformation. We find that a linear decoder operating on the responses of this Maximum Variance Differentiation (MVD) model attains target match vs. distractor performance close to that of an ideal observer operating on the IT population, and far better than a linear decoder operating directly on the input IT population, suggesting that most of the target match information embedded in IT population responses lies in the class variances. Furthermore, the MVD population matched Perirhinal linear decoder performance, suggesting that an MVD transformation within Perirhinal cortex may act on input arriving from IT. These results provide evidence that within the family of LNL models, a generalization of the Energy model is sufficient to explain the untangling of visual target match information.