An experimental campaign was undertaken to measure the pedestrian flow in the region close to the Kaaba during the Hajj pilgrimages of 2014 and 2015. High resolution video and photographs were used. The space was divided into areas of 10 sqm. The pedestrians were counted, and the velocity measured from video clips. The results were surprising: the velocity in the very high density region increases, which implies also an increase of the flux. The flux in this region (with more than 8p/sqm) reaches values that exceed 3.5 p/m/sec, much higher than previously recorded under more `standard conditions' in corridors and passages.