The experiment aims at the simultaneous determination of the two transversal polarization components of electrons emitted in the decay of free, polarized neutrons. A non-zero value of R due to the polarization component, which is perpendicular to the plane spanned by the spin of the decaying neutron and the electron momentum, would signal a violation of time reversal symmetry and thus physics beyond the Standard Model (SM). The value of N, given by the transverse polarization component within that plane, is expected to be finite. The measurement of N both probes the SM and serves as an important systematic check of the apparatus for the R-measurement. We estimate that such an experiment is feasible with an accuracy of 0.005 within a few weeks of data taking time on the polarized cold neutron beam line of the spallation source SINQ at PSI, Villigen, Switzerland. This will be the first such measurement for the decay of free neutrons, bearing a potential to detect either a non-standard value or to provide important constraints for the scalar and tensor couplings in the semileptonic weak interactions.