  A remarkable result of the Wilkinson Microwave Anisotropy Probe (WMAP)
observations is that the universe was significantly reionized at large
redshifts. The standard explanation is that massive stars formed early and
reionized the universe around redshift z=17. Here we explore an alternative
possibility, in which the universe was reionized in two steps. An early boost
of reionization is provided by a decaying sterile neutrino, whose decay
products, relativistic electrons, result in partial ionization of the smooth
gas. We demonstrate that a neutrino with a mass of m_nu ~ 200 MeV and a decay
time of t ~ 4 * 10^{15} s can account for the electron scattering optical depth
tau=0.16 measured by WMAP without violating existing astrophysical limits on
the cosmic microwave and gamma ray backgrounds. Reionization is then completed
by subsequent star formation at lower redshifts. This scenario alleviates
constraints on structure formation models with reduced small-scale power, such
as those with a running or tilted scalar index, or warm dark matter models.
