Very Long Baseline Radio Interferometery (VLBI) usually involves the use of an independent time standard at each of the widely dispersed array elements. The standard practice is to correlate the signals from each pair of antennas over a range of time lags, and then to determine the difference in the 'clock errors' (delay) and the difference in the first time derivative (fringe rate). The present investigation is concerned with an alternative to the standard correlator-based fringe search technique. A global approach which yields a simultaneous solution for all of the delay and fringe rate parameters is provided. For each base line, each delay or rate parameter splits into two components, ascribable to two individual antennas. It is pointed out that the global fringe search approach may be viewed as a variant of the self-calibration/hybrid mapping techniques which are in widespread use in aperture synthesis data reduction.