A new hierarchical method to determine molecular similarity is introduced. The goal of this method is to detect if a pair of molecules has the same structure by estimating a rigid transformation that aligns the molecules and a correspondence function that matches their atoms. The algorithm firstly detect similarity based on the global spatial structure. If this analysis is not sufficient, the algorithm computes novel local structural rotation‐invariant descriptors for the atom neighborhood and uses this information to match atoms. Two strategies (deterministic and stochastic) on the matching based alignment computation are tested. As a result, the atom‐matching based on local similarity indexes decreases the number of testing trials and significantly reduces the dimensionality of the Hungarian assignation problem. The experiments on well‐known datasets show that our proposal outperforms state‐of‐the‐art methods in terms of the required computational time and accuracy. © 2015 Wiley Periodicals, Inc. The proposal tackles hierarchically the detection of molecular similarity. First, global structure information is computed to align the molecules and determine their similarity: as for instance the blue‐green‐red inertia axes. When the global analysis fails, novel local rotation‐invariant descriptors are atom‐wise computed to estimate atom‐to‐atom similarity (matchings): the atoms' color in molecule B indicates their local similarity to the highlighted jth atom in molecule A; the actual corresponding atom in B is also highlighted.