We propose a new algorithm to determine reaction paths and test its capability for Ar12 and Ar13 clusters. Its main ingredient is a search for the local minima on a (n−1) dimensional hyperplane (n = dimension of the complete system in Cartesian coordinates) lying perpendicular to the straight line connection between initial and final states. These minima are part of possible reaction paths and are, hence, used as starting points for an uphill search to the next transition state. First, path fragments are obtained from subsequent relaxations starting from these transition states. They can be combined with information from the straight line connection procedure to obtain complete paths. Our test computations for Ar12 and Ar13 clusters prove that PathOpt delivers several reaction paths in one round. © 2013 Wiley Periodicals, Inc.