In this paper we establish the definition of the set of ε-proper equilibria of a bimatrix game. We define a 0-1 mixed quadratic program to generate a sequence of ε-proper Nash equilibria and show that the optimization results provide reliable indications on strategy profiles that could be used to generate proper equilibria analytically. This approach can be generalized in order to find at least one proper equilibrium for any bimatrix game. Finally, we define another 0-1 mixed quadratic program to identify non-proper extreme Nash equilibria.