  The Tanaka equation $dX_t={\operatorname{sign}}(X_t)\,dB_t$ is an example of
a stochastic differential equation (SDE) without strong solution. Hence
pathwise uniqueness does not hold for this equation. In this note we prove that
if we modify the right-hand side of the equation, roughly speaking, with a
strong enough additive noise, independent of the Brownian motion B, then the
solution of the obtained equation is pathwise unique.
