In this paper, we introduce a Shared Multiple Rooted XOR-based Decomposition Diagram (XORDD) to represent functions with multiple outputs. Based on the XORDD representation, we develop a synthesis algorithm for general Exclusive Sum-of-Product forms (ESOP). By iteratively applying transformations and reductions, we obtain a compact XORDD which gives a minimized ESOP. Our method can synthesize larger circuits than previously possible. The compact ESOP representation provides a form that is easier to synthesize for XOR heavy multi-level circuits, such as arithmetic functions. We have applied our synthesis techniques to a large set of benchmark circuits in both PLA and combinational formats. Results of the minimized ESOP forms obtained from our synthesis algorithm are also compared to the SOP forms generated by ESPRESSO. Among the 74 circuits we have experimented with, the minimized ESOP's have fewer product terms than those of SOP's in 39 circuits.