Let H = Q.(ζn +ζn-1) and ℓ be an odd prime such that q ≅ 1 .mod ℓ/ for a prime factor q of n. We get a bound on the ℓ-rank of the class group of H in terms of the ℓ-rank of the class group of a real quadratic subfield contained in H. At the end we look into few numerical examples.