The utilization of EXOR gates often decreases the number of gates needed for realizing practical logical networks, and enhances the testability of networks. Therefore, logic synthesis with EXOR gates has been studied. In this paper we propose a new logic representation: an ESPP (EXOR-Sum-of-Pseudoproducts) form based on pseudoproducts. This form provides a new three-level network with EXOR gates. Some functional classes in ESPP forms can be realized with shorter expressions than in conventional forms such as the Sum-of-Products. Since many practical functions have the properties of such classes, the ESPP form is useful for making a compact form. We propose a heuristic minimization algorithm for ESPP, and we demonstrate the compactness of ESPPs by showing our experimental results. We apply our technique to some logic function classes and MCNC benchmark networks. The experimental results show that most ESPP forms have fewer literals than conventional forms.