To improve the unrestricted second-order Moller-Plesset (UMP2) method, we propose a method in which spin contamination is eliminated due to spin adaptation of the double excitation space based on the unitary group approach (UGA), because the UMP2 calculations intrinsically involve spin contamination from the double excitation space. Numerical results for the activation energies of several radical reactions show that this UGA-UMP2 method offers substantial improvement over the UMP2 method. Furthermore, the UGA-SUMP2 method, which completely eliminates the spin contamination from both the reference and excitation space present in UMP2 calculations, is also formulated. (C) 2016 Elsevier B.V. All rights reserved.