Observations of angles or distances between stations of a geodetic network are commonly used to infer information about the movement of the surface of the earth. The absence of any observations external to the network leads to an ambiguous displacement field. Existing techniques for eliminating this ambiguity are all unsatisfactory in some respect. The best technique, an ''inner coordinate'' solution, is not appropriate for networks located in a strike slip fault enviroment. The inner coordinate solution zeros the rotation of all stations about their center of mass. Along a strike slip fault like the San Andreas, however, motion normal to the fault is less likely than motion parallel to the fault. The solution presented here, an ''outer coordinate'' solution, finds the rotation of the network that minimizes the components of displacment normal to the fault. Since motion along a strike slip fault is generally expected to be parallel to the fault, the displacements obtained with the outer coordinate solution are more reasonable than those obtained with other techniques. Examination of a trilateration network near San Francisco Bay demonstrates the large effect that the choice of adjustment technique can have on the inferred relative motion of the two sides of the fault. The inner coordinate solution gave a rate of about 1 mm/yr, whereas the preferred outer coordinate solution rate was 36 mm/yr.