Acceleration of electrons to relativistic energies by a multidimensional self-modulated laser wakefield is discussed. Above a power threshold, a relativistically self-guided channel from an intense ultrashort laser pulse ( $I\ensuremath{\sim}4\ifmmode\times\else\texttimes\fi{}{10}^{18}\mathrm{W}/{\mathrm{cm}}^{2}$, $\ensuremath{\lambda}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1\ensuremath{\mu}\mathrm{m}$, $\ensuremath{\tau}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}400\mathrm{fs}$) was found to increase the laser propagation distance, decrease the electron beam divergence, and increase the energy of the electrons. These electron beam effects occurred even though the propagation distance became significantly longer than the conventional dephasing length.