  We investigate the non-Markovian characteristics in continuous measurement of
a charge qubit by a quantum point contact. The backflow of information from the
reservoir to the system in the non-Markovian domain gives rise to strikingly
different qubit relaxation and dephasing in comparison with the Markovian case.
The intriguing non-Markovian dynamics is found to have a direct impact on the
output noise feature of the detector. Unambiguously, we observe that the
non-Markovian memory effect results in an enhancement of the signal-to-noise
ratio, which can even exceed the upper limit of ``4'', leading thus to the
violation of the Korotkov-Averin bound in quantum measurement. Our study thus
may open new possibilities to improve detector's measurement efficiency in a
direct and transparent way.
