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We investigate the transport equation ${\partial }_{t}u(t,x)+b(t,x)·D_{x}u(t,x)=0$. Our result improves the classical criteria of uniqueness of weak solutions in the case of irregular coefficients: b ∈ BV, $di{v}_{x}b\in BMO$. To obtain our result we use a procedure similar to DiPerna and Lions’s one developed for Sobolev vector fields. We apply renormalization theory for BV vector fields and logarithmic type inequalities to obtain energy estimates.