Both components of the transverse polarization of electrons (σT 1 , σT 2 ) emitted in the β-decay of polarized, free neutrons have been measured. The T-odd, P-odd correlation coefficient quantifying σT 2 , perpendicular to the neutron polarization and electron momentum, was found to be R = 0.008±0.015±0.005. This value is consistent with time reversal invariance, and significantly improves limits on the relative strength of imaginary scalar couplings in the weak interaction. The value obtained for the correlation coefficient associated with σT 1 , N = 0.056±0.011±0.005, agrees with the Standard Model expectation, providing an important sensitivity test of the experimental setup.PACS numbers: 24.80.+y, 23.40.Bw, 24.70.+s, 11.30.Er Despite the great success of the Standard Model (SM) of elementary particles and their interactions, several important questions remain open. One of these is the incomplete knowledge of physics of CP-violation, or via the CPT theorem, time reversal symmetry violation (TRV). The SM with the Cabbibo-Kobayashi-Maskawa (CKM) mixing scheme accounts for CP violation discovered in kaon [1] and B-meson [2, 3] systems. It fails, however, to explain the basic observation of the dominance of matter in the present Universe. The discovery of new CPor T-violating phenomena, especially in systems built of light quarks with vanishingly small contributions of CKM matrix induced mechanisms, would be a major breakthrough. Nuclear beta decay experiments test these systems and free neutron decay plays a particular role: due to its simplicity it is free of corrections associated with the nuclear and atomic structure. Further, final state interaction effects, which can mimic T violation, are minimal and can, in addition, be calculated with a relative precision better than 1% [4].In this Letter we report on the first experiment searching for the real and imaginary parts of scalar and tensor couplings via the measurement of the transverse polarization of electrons emitted in the decay of free neutrons. There exist very few measurements of this observable in general [5,6], and only two in nuclear beta decays. One of them, for the 8 Li system [7], provides the most stringent limit on tensor coupling constants of the weak interaction.According to [8], the decay rate distribution as a function of electron energy (E) and momentum (p), from polarized neutrons is proportional to:where J is the neutron spin,σ is a unit vector onto which the electron spin is projected and A is beta decay asymmetry parameter. N and R are correlation coefficients which, for neutron decay with the SM assumptions, and allowing for a small admixture of scalar and tensor couplings C S , C T , C ′ S , C ′ T , can be expressed as:whereT )/C A and m is the electron mass. The R correlation value vanishes to the lowest order within the SM. Including final state interactions it becomes different from zero, R F SI ≈ 0.0006, still below the sensitivity of the present experiment. A larger measured value would provide a hint for the existence of exo...