Neutralino Contribution to the Mass Difference of $B_d^0-\bar B_d^0$

We present a detailed and complete calculation of the neutralino contribution to the mass difference $\Delta m_{B_d^0}/m_{B_d^0}$\ within the MSSM. We include the complete mixing matrices of the neutralinos and of the scalar partners of the left and right handed bottom quark. We find that the neutralino contribution is generally small but can be of the same order of the chargino contribution and much larger than that of the gluino over a small range of $m_S$, given $m_{g_2}$ and $\mu$ and for $\tan\beta\sim 50$.