  We study the decoherence of a single electron spin in an isolated quantum dot
induced by hyperfine interaction with nuclei for times smaller than the nuclear
spin relaxation time. The decay is caused by the spatial variation of the
electron envelope wave function within the dot, leading to a non-uniform
hyperfine coupling $A$. We show that the usual treatment of the problem based
on the Markovian approximation is impossible because the correlation time for
the nuclear magnetic field seen by the electron spin is itself determined by
the flip-flop processes.
  The decay of the electron spin correlation function is not exponential but
rather power (inverse logarithm) law-like. For polarized nuclei we find an
exact solution and show that the precession amplitude and the decay behavior
can be tuned by the magnetic field. The decay time is given by $\hbar N/A$,
where $N$ is the number of nuclei inside the dot. The amplitude of precession,
reached as a result of the decay, is finite. We show that there is a striking
difference between the decoherence time for a single dot and the dephasing time
for an ensemble of dots.
