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The exact boundary controllability of the non-linear Korteweg-de Vries equation on bounded domains is studied. Only the first spatial derivative at the right endpoint is assumed to be controlled. In this case, the exact controllability has been shown by Rosier (1997) when the length L of the domain is not in the set N:= {2πradic;(k[sup 2]+kl+l[sup 2])/3;k, l ∈ N*}. Here, we study the critical case L=2kπ where k ∈ N*, and we prove the exact controllability of the non-linear KdV equation for initial and final states closed to a non-null small stationary solution. [ABSTRACT FROM AUTHOR]