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 observations between them and a common object observed by both vehicles is presented. The constraint may either be a planar constraint or triangle constraint of the observed vectors. The differences between both are shown. Either constraint allows for a solution without having toknowthe location of thecommonobject. Thepresented solution with the constraint represents theminimum number of measurements required to determine the relative attitude 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. A sensitivity analysis is also performed in order to assess how out-of-plane observations affect the overall solution. Simulation results are provided to assess the performance of the proposed new approach.