  We present the perturbative matching coefficient to $O(a\alpha_s)$ which
relates the $\Delta B$=2 operator in the continuum to that of the lattice
static theory, which is important in the accurate extraction of the continuum
value of the $B_B$ from lattice simulations. The coefficients are obtained by
the one-loop calculations in both of the continuum and lattice theory. We find
that two new dimension seven operators appear at the $O(a\alpha_s)$ with the
O(1) coefficients. We also discuss the possible cancellation of $O(a\alpha_s)$
correction in the ratio $B_B=<\bar{B}|\Op_L|B>/ ((8/3)(f_{B}M_{B})^2)$
qualitatively.
