High-resolution echelle spectra have been obtained of the semi-detached Algol-type eclipsing binary system, TX UMa with the high-resolution echelle spectrographs of the 1.8 m telescope at Bohyunsan Optical Astronomy Observatory in Korea and of the 2.0 m telescope of Peak Terskol Observatory in Russia. New accurate radial velocities of its components have been measured. With the new measurements, we have been able to infer an improved orbital solution and the masses of the components of the system. For the first time, we have measured the rotational velocity for the Roche lobe filling secondary component. We have concluded that it rotates synchronously, while the rotation of the mass-accreting primary component is 1.5 times faster than synchronous. TX UMa confirms the previous conclusion that the strong lines of the light elements (N, O, Mg) in the atmospheres of mass-accreting components in Algol-type systems are stronger and wider than in single stars of the same spectral class and luminosity. Stronger lines also imply higher elemental abundances than weak lines, but this can also be explained if the former have greater microturbulent velocities. We have suggested that such an excess enhancement of the strong lines may be explained in terms of a distended pseudo-atmosphere of the mass-accreting component, engendered by gas flowing in via the L1 Lagrange point. We have found the chemical abundances of 12 elements in the atmosphere of the primary component of TX UMa. Si and Ni were found to show significant deficiencies while the abundance measures of C varied (within the uncertainties of the model atmosphere parameters) from solar to noticeably deficient. Other elements, including He, have solar abundance. The abundances of the secondary component are likely solar, as its spectrum is represented well by a synthetic spectrum with solar abundance and Teff= 5500 K and log g = 3.3.