Tanaka's formula is the following result $$|B_t| = \int_0^t \text{sgn}(B_s)\, dB_s + L_t$$
I can see how to show that the stochastic integral $$M_t = \int_0^t \text{sgn}(B_s)\, dB_s$$ is a martingale (by the Levy characterization).
It seems to me intuitively, though, that this integral can never take a negative value. Considering (admittedly finite variation and differentiable) linear sample paths, the result of this integral is (I think) $|B_t|$. Considering piece-wise linear sample paths is similar, though the value of the integral can at least decrease as $t$ increases, but seemingly never below 0.
So my question is, what is a possible sample path of $B$ where the stochastic integral $M$ takes a negative value at some time?