This paper studies constrained relative attitude determination of a formation of two vehicles. A deterministic solution for the relative attitude between the two vehicles with line-of-sight measurements between them and a common object observed by both vehicles is presented. The solution represents the minimum number of measurements required to determine the relative attitudes and no ambiguities are present. To quantify the performance of the algorithm the covariance of the attitude error is derived using a linearized error model from a least-squares point of view. Simulation results are also provided to assess the performance of the proposed new approach.