The formal framework of the recently developed infinite-order two-component (IOTC) method of relativistic quantum chemistry is analysed. The former iterative scheme of the IOTC approach is replaced by the non-iterative method which leads to the complete block-diagonalization of the algebraic Dirac Hamiltonian and permits to built the matrix representation of the equivalent two-component one-electron energy operator. The method is equivalent to solving the so-called non-symmetric algebraic Riccati equation. Its solution is illustrated numerically. (C) 2007 Elsevier B.V. All rights reserved.