We present constraints on the mass of warm dark matter (WDM) particles derived from the Lyman-alpha flux power spectrum of 55 high-resolution HIRES spectra at 2.0<z<6.4. From the HIRES spectra, we obtain a lower limit of m(WDM) > or approximately 1.2 keV (2sigma) if the WDM consists of early decoupled thermal relics and m(WDM) > or approximately 5.6 keV (2sigma) for sterile neutrinos. Adding the Sloan Digital Sky Survey Lyman-alpha flux power spectrum, we get m(WDM) > or approximately 4 keV and m(WDM) > or approximately 28 keV (2sigma) for thermal relics and sterile neutrinos. These results improve previous constraints by a factor of 2.