Abstract: This paper puts forward a new method of rapid ambiguity resolution for single-frequency GPS receivers.The new method needs not resolve float solutions of ambiguities and also uses the integer Gauss transformation technique like LAMBDA method. Its principle is that the total sums of squares of residuals in sequence is expressed as a quadratic of the function of integer ambi-guity, then a suitable searching space is constructed through the integer Gauss transformation, and a point is searched whose whole sum of squares of residuals is the least by using a method of the reordering of the conditional variances. Using this method, when new observations need be added, it is not necessary to process all of the old and new observations but only to calculate the changes of the residues caused by the new observations, which decreases the memory and the time of resolution and also improves the conditions of the search space of ambiguities. Therefore, determining the ambiguities by the new method is rapider than by other methods. The numerical results of experiments on different length baselines show that the new method is rapid and stable in relative positioning with single-frequency GPS receivers.