Equidistant Uniform Rigid-body Ensemble CONstructor. Here we presented a fast algorithm for the construction of rigid-body conformational ensembles, which possess two main properties: i) each generated conformation has a fixed RMSD with respect to the original conformation, ii) generated conformations are distributed uniformly over the sphere of axes corresponding to the rigid-body motions. The algorithm is very efficient, it does not require any standard RMSD computation between the conformations and has the O(N+M) complexity to generate the required rigid-body transforms, where N is the number of atoms in the system, and M is the size of the conformational ensemble. Eurecon is applicable to an arbitrary atomic system, thus, it could be used for molecular systems of various size and type.