In this Letter, a new fractional entangling transformation （FRET） is proposed, which is generated in the entangled state representation by a unitary operator exp{iθ（ab^＋ ＋ a^＋ b）} where a（b） is the Bosonic annihilate operator. The operator is actually an entangled one in quantum optics and differs evidently from the separable operator, exp（iθ（a^＋a＋ b^＋ b）}, of complex fractional Fourier transformation. The additivity property is proved by employing the entangled state representation and quantum mechanical version of the FRET. As an application, the FrET of a two-mode number state is derived directly by using the quantum version of the FRET, which is related to Hermite polynomials.
