The homology and cohomology of invariant group chains have been defined by Kevin Knudson. Later, we introduce the invariant cohomology of a Q-group G with coefficients in a Q-G module M, denoted by \(HH^{*}_{Q}(G,M)\) . In this paper we prove that we can replace the bar resolution \(B_{*}(G)\) by the normalized bar resolution \(B_{*}^{N}(G)\) to calculate the invariant cohomology. In this way, the modules that make up the normalized bar resolution are free Q-G modules when the action of Q on G is free. Using this normalized bar resolution, we construct a spectral sequence converging to \(HH^{*}_{Q}(G,M)\) and finally, with this spectral sequence we prove that the invariant cohomology is not equal, in general, to the cohomology of the group \(G\rtimes Q\) .
