We prove that the beam equation with clamped ends is locally controllable in a H(5+epsilon) x H(3+epsilon) ((0, 1), R)-neighborhood of a particular trajectory of the free system, with epsilon > 0 and with control functions in H(0)(1) ((0, T), R). Ball,. Marsden, and Slemrod already proved that this equation is not controllable in H(0)(2) x L(2)((0, 1), R) with control functions in L(loc)(r)( R, R), r > 1. This article justifies that their negative result is due to a choice of functional spaces which does not allow controllability. Our proof uses moment theory and the Nash-Moser theorem.