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In this short note, we consider bilinear pseudo-differential operators withsymbols belonging to the Sj\"ostrand class. We show that those operators arebounded from the product of the $L^2$-based Sobolev spaces $H^{s_1} \timesH^{s_2}$ to $L^r$ for $s_1,s_2 > 0$, $s_1+s_2=n/2$, and $1 \leq r \leq 2$.

A remark on bilinear pseudo-differential operators with symbols in the Sj\"ostrand class