  We discuss the coherent search strategy to detect gravitational waves from
inspiraling compact binaries by a network of correlated laser interferometric
detectors. From the maximum likelihood ratio statistic, we obtain a coherent
statistic which is slightly different from and generally better than what we
obtained in our previous work. In the special case when the cross spectrum of
two detectors normalized by the power spectrum density is constant, the new
statistic agrees with the old one. The quantitative difference of the detection
probability for a given false alarm rate is also evaluated in a simple case.
