A generalization of the shape-consistent Relativistic Effective Core Potential (RECP) method is developed for the case of pseudospinors that may have nodes. Both valence and outermost core pseudospinors are included in the Generalized RECP generation procedure. The numerical potentials have been constructed and the calculations of transition energies and some other properties have been made for the atoms Hg through Bi in the jj-coupling scheme in order to study the treatment of relativistic effects in the scope of the two-component Generalized RECP approach. As compared with the other shape-consistent RECP variants, significant improvement is reached when 5s, 5p, and 5d shells are included in the pseudovalence space.