Markov Property, running maximum of Brownian Motion.

Question

Let $B = (B_t)_{t \geqslant 0}$ be standard Brownian motion. Set $$X_t = \max_{0 \leqslant s \leqslant t} B_s, \ \text{for} \ t \geqslant 0.$$

Is $X= (X_t)_{t\geqslant 0} $ a Markov Process with respect to its natural filtration?