Development of alternative methods for hydrogen production from liquid water requires novel research approaches. In the present study, we investigated the yet unexplored method of water splitting by femtosecond laser pulses (100 fs, lambda = 800 nm) focused into a quartz cell containing ultra-purified water. As a result of plasma induced radical reactions, the formation of stable products including molecular H-2 and H2O2 was identified and quantified as a function of irradiation time, repetition rate and pulse energies up to 1 mJ. The observed dependencies provided new insight into the basic chemical processes taking place in the plasma generated in water by focused laser pulses. It was found that the energy efficiency of hydrogen production increased with the decrease of pulse energy and repetition rate. Under appropriate irradiation conditions, an advantageous stoichiometry of water decomposition only into pure H-2 and H2O2 (without O-2) was achieved. An original way of process intensification (a series of separate laser beams of adequately low energy generating plasma at different places, a sufficiently fast water flow through the irradiation zones) was proposed in order to improve the energy yield of hydrogen generation and to ensure the evolution of pure hydrogen as the only gaseous product of the water splitting. Taking into account the suggested solution, the predicted energy efficiency of hydrogen production of 0.4 g H-2/kWh was found to be comparable to other plasma methods for H-2 generation. Our results show that direct production of pure H-2 using femtosecond laser pulses is a fully reasonable process that carries considerable potential for both research and application.