# Strong markov property of a transformation of the Brownian motion

Let $$(B_t)$$ be a standard Brownian motion and consider $$(X_t)$$ defined as: $$X_t=e^{-t}B_{e^{2t}}$$ I've proved that this process is markov, however I can't prove that is strong markov. I know that this seem like the Ornstein-Uhlenbeck process but I don't know anything about SDE that probably will solve this problem easly.