The BSE Sensex fell on Wednesday, easing for a second consecutive session, as blue chips such as Tata Motors and software services exporters declined on profit-taking. The Sensex fell 0.47 per cent, or 97.09 points, to end at 20,767.88, retreating for a second day after marking its highest level since November 2010 on Monday. The broader Nifty fell 0.39 per cent, or 24.45 points, to end at 6,178.35, falling for a consecutive session.