Multi-spacecraft missions like the ESA mission CLUSTER and the NASA mission MMS are essential to improve our understanding of physical processes in space plasmas. Several methods were designed in the 90's during the preparation phase of the CLUSTER mission to estimate gradients of physical fields from simultaneous multi-points measurements [1, 2]. Both CLUSTER and MMS involve four spacecraft with identical full scientific payloads including various sensors of electromagnetic fields and different type of particle detectors. In the standard methods described in [1, 2], which are presently in use, data from the four spacecraft have identical weights and the estimated gradients are most reliable when the tetrahedron formed by the four spacecraft is regular. There are three types of errors affecting the estimated gradients (see chapter 14 in [1]) : i) truncature errors are due to local non-linearity of spatial variations, ii) physical errors are due to instruments, and iii) geometrical errors are due to uncertainties on the positions of the spacecraft. An assessment of truncature errors for a given observation requires a theoretical model of the measured field. Instrumental errors can easily be taken into account for a given geometry of the cluster but are usually less than the geometrical errors which diverge quite fast when the tetrahedron flattens, a circumstance occurring twice per orbit of the cluster. Hence reliable gradients can be estimated only on part of the orbit. Reciprocal vectors of the tetrahedron were presented in chapter 4 of [1], they have the advantage over other methods to treat the four spacecraft symmetrically and to allow a theoretical analysis of the errors (see chapters 4 of [1] and 4 of [2]). We will present Generalized Reciprocal Vectors for weighted data and an optimization procedure to improve the reliability of the estimated gradients when the tetrahedron is not regular. A brief example using CLUSTER or MMS data will be given. This approach also operates for any number of spacecraft. References [1] Analysis Methods for Multi-Spacecraft Data, ISSI Scientific Report, SR-001, Eds. G. Paschmann and P.W. Daly, ISSI, Bern, Switzerland, 1998. [2] Multi-Spacecraft Analysis Methods Revisited, ISSI Scientific Report, SR-008, Eds. G. Paschmann and P.W. Daly, ISSI, Bern, Switzerland, 2008.