The rank dependence of orientational relaxation is investigated in model Brownian dipolar lattice using the projection operator formalism. The contribution of long range dipolar interactions to the rate of single particle orientational relaxation is evaluated perturbatively in terms of the polarity parameter of the system. Analytical expressions, exact up to second order, for the general rank dependent, single particle orientational correlation function are presented. It is found that the frequency term in the equation of motion of the single particle orientational correlation function does not depend on dipolar interactions when evaluated up to the second order term. The memory function, on the other hand, derives significant contributions from the dipolar interactions. Relaxation of orientation of rank l is found to become nonexponential due to coupling with those of ranks l - 1 and l + 1, and this becomes more pronounced in the limit of strong interaction. The theoretical predictions are corroborated well by the known computer simulation results.