Upstream from the supernova quasiparallel shock wave, the hot component representing cosmic rays is locked at the shock front due to scattering by magnetic field fluctuations, and is accelerated by the diffusive shock acceleration mechanism. The cosmic ray population, isotropic in the shock frame and drifting with the shock velocity relative to the interstellar plasma, is shown to be unstable with respect to a nonresonant beam type electromagnetic instability similar to a firehose mode. Solution of the dispersion relation for this instability is obtained using both analytical and numerical methods. For a power-like distribution of the cosmic ray particles, f(ϵ)~ϵ-2, an expected consequence of diffusive shock acceleration, the maximum growth rate of the magnetic fluctuations corresponds to wavelengths that are significantly greater than the gyroradius at the upper edge of the energy spectrum. Because such extremely long fluctuations tangle magnetic field lines, diffusion of the cosmic ray particles increases significantly, resulting in an essential extension of the energy range for diffusive shock acceleration. ¿ 1998 American Geophysical Union