We give a short report on the possibility to use orthogonal polynomials (OP) in calculations that involve the two-nucleon (2N) transition operator. The presented work adds another approach to the set of previously developed methods (described in Phys. Rev. C 81, 034006 (2010); Few-Body Syst. 53, 237 (2012); K. Topolnicki, PhD thesis, Jagiellonian University (2014)) and is applied to the transition operator calculated at laboratory kinetic energy 300MeV. The new results for neutron-neutron and neutron-proton scattering observables converge to the results presented in Few-Body Syst. 53, 237 (2012) and to results obtained using the Arnoldi algorithm (Y. Saad, Iterative methods for sparse linear systems (SIAM Philadelphia, PA, USA 2003)). The numerical cost of the calculations performed using the new scheme is large and the new method can serve only as a backup to cross-check the previously used calculation schemes.