In future most global positioning system (GPS) carrier phase observation campaigns will be conducted with more than 2 receivers operating at the same time. This fact is of importance for those processing algorithms using the so called single- or double-differences as basic observable, since all single- (and double-) differences referring to one and the same epoch are mathematically correlated. In this paper we present an efficient algorithm to compute the inverse of the covariance matrix taking these correlations for double difference observations into account.