The existence and uniqueness of positions computed from Global Positioning System (GPS) pseudorange measurements is studied. Contrary to the claims of Bancroft (1985) and Krause (1987), in the case of n = 4 satellites a fix may not exist, and, if a fix exists, it is not guaranteed to be unique. In the case of n = more than 5 satellites, a unique fix is assured, except in certain degenerate cases such as coplanar satellites. Finally, an alternate formulation of the direct n = 4 pseudorange to three-space position solutions of Bancroft and Krouse is presented, and simple tests for existence and uniqueness are derived.