The stability of doubly quantized vortices in dilute Bose-Einstein condensates is examined at zero temperature. The eigenmode spectrum of the Bogoliubov equations for a harmonically trapped cigar-shaped condensate is computed and it is found that the vortex is spectrally unstable. The emerging complex eigenvalues correspond to the splitting of the vortex, which is analyzed by numerically solving the full three-dimensional time-dependent Gross-Pitaevskii equation.