A process for alkaline hydrogen peroxide bleaching of mechanical wood pulp which employs a quaternary amine compound, such as (3-chloro-2-hydroxypropyl)trimethyl ammonium chloride, in the stabilized bleach solution. The brightness of the final paper product made from such bleached pulp shows marked improvement over that in which only chelating agents are employed to improve the brightness according to the known art. The process is useful in both silicate and silicate-free bleach solutions.