Fundamental observational programs are often lengthened because of the sparsity of data during bad weather seasons and the need of having strong links all over the 24h of right ascension. The global reduction procedure tries to minimize this problem by making more efficient use of the available information with full consideration of incomplete or isolated group observations. The whole set of observational material is treated as a single least squares problem, whose unknowns include corrections to the star positions. The problem is usually of huge dimensions, but we show that it can be reduced to quite tractable sizes. As an example, the method is applied to a two year series of astrolabe observations. The time and latitude curves are solved for under the form of cubic spline functions. The results are equivalent to those of conventional procedures, provided due account is given to the fact that, in the global reduction, long period components of image motion are fully included in the standard error estimates.