  We have derived explicit non-perturbative expression for decoherence of
quantum oscillations in a qubit by low-frequency noise. Decoherence strength is
controlled by the noise spectral density at zero frequency while the noise
correlation time $\tau$ determines the time $t$ of crossover from the
$1/\sqrt{t}$ to the exponential suppression of coherence. We also performed
Monte Carlo simulations of qubit dynamics with noise which agree with the
analytical results and show that most of the conclusions are valid for both
Gaussian and non-Gaussian noise.
