In Theorem 3.3 of [I. Biswas and P. Chatterjee, On the exactness of Kostant-Kirillov form and the second cohomology of nilpotent orbits, Int. J. Math. 23(8) (2012)], the second cohomology of a quotient of a compact semisimple real Lie group was computed. In this addendum to the above paper, we give a simple topological proof of this theorem.