In this note, we obtain the expression of the characteristic fucntion of the random variable $int_o^TB_s^{{alpha},{eta}}dB_s^{H,K}$, where $B^{{alpha},{eta}}$ and $B^{H,K}$ are two independent bifractional Brownian motions with indices ${alpha}{in}(0,1),{eta}{in}(0, 1]$ and $HK{in}(frac{1}{2},;1)$ respectively.