  The statistical properties of estimator using covariance matrix for the
account of point-to-point correlations due to systematic errors are analyzed.
It is shown that the covariance matrix estimator (CME) is consistent for the
realistic cases (when systematic errors on the fitted parameters are not
extremely large comparing with the statistical ones) and its dispersion is
always smaller, than the dispersion of the simplified $\chi^2$ estimator
applied to the correlated data. The CME bias is negligible for the realistic
cases if the covariance matrix is calculated during the fit iteratively using
the parameter estimator itself. Analytical formula for the covariance matrix
inversion allows to perform fast and precise calculations even for very large
data sets. All this allows for efficient use of the CME in the global fits.
