Studying the motion of Lennard-Jones clusters in an external potential having a very narrow channel passage at the saddle point, we present a one-point boundary scheme to numerically sample transition (reaction) paths. This scheme does not require knowledge of the transition states (saddle points) or that of the final states. A transition path within a given time interval (0, t(f)) consists of an activation path during (0,t(M)) and a deactivation path during (t(M),t(f)) (0