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Let k be an algebraically closed field of characteristic zero, H a semisimple Hopf algebra of dimension pq² of Frobenius type, where p, q are distinct prime numbers. This paper proves that if p > q and H^* is also of Frobenius type then H is a biproduct of a group algebra A of dimension q² and a Yetter-Drinfeld Hopf algebra R over A of dimension p. That is H ≌ R#A. As an example, this paper then proves that every semisimple Hopf algebra of dimension 63 or 68 is of Frobenius type.