R Canis Majoris is the prototype of a small group of Algol-type stars showing short orbital periods and low mass ratios. A previous detection of short-term oscillations in its light curve has not yet been confirmed. We investigate a new time series of high-resolution spectra with the aim to derive improved stellar and system parameters, to search for the possible impact of a third component in the observed spectra, to look for indications of activity in the Algol system, and to search for short-term variations in radial velocities. We disentangled the composite spectra into the spectra of the binary components. Then we analysed the resulting high signal-to-noise spectra of both stars. Using a newly developed program code based on an improved method of least-squares deconvolution, we were able to determine the radial velocities of both components also during primary eclipse. This allowed us to develop a better model of the system including the Rossiter-McLaughlin effect and to derive improved orbital parameters. Combining the results with those from spectrum analysis, we obtain accurate stellar and system parameters. We further deduce at least one oscillation frequency of 21.38c/d. It could be detected during primary eclipses only and confirms a previous photometric finding. Results point to an amplitude amplification of non-radial pulsation modes due to the eclipse mapping effect. The presence of a HeI line in the spectra indicates mass transfer in the R CMa system. Calculations of its Roche geometry give evidence that the cool secondary component may fill its Roche lobe. No evidence of a third body in the system could be found in the observed spectra.