Wolf A Reiher M 2006 In Part III [J. Chem. Phys. 124, 064102 (2005)] of this series of papers on exact decoupling of the Dirac Hamiltonian within transformation theory, we developed the most general account on how to treat magnetic and electric properties in a unitary transformation theory on the same footing. In this paper we present an implementation of a general algorithm for the calculation of magnetic as well as electric properties within the framework of Douglas-Kroll-Hess theory. The formal and practical principles of this algorithm are described. We present the first high-order Douglas-Kroll-Hess results for property operators. As for model properties we propose to use the well-defined radial moments, i.e., expectation values of r(k), which can be understood as terms of the Taylor-series expansion of any property operator. Such moments facilitate a rigorous comparison of methods free of uncertainties which may arise in a direct comparison with experiment. This is important in view of the fact that various approaches to two-component molecular properties may yield numerically very small terms whose approximate or inaccurate treatment would not be visible in a direct comparison to experimental data or to another approximate computational reference. Results are presented for various degrees of decoupling of the model properties within the Douglas-Kroll-Hess scheme. https://sonar.ch/global/documents/47243 eng info:eu-repo/semantics/altIdentifier/doi/10.1063/1.2161180 info:eu-repo/semantics/altIdentifier/pmid/16483192 The Journal of chemical physics. - 2006 Exact decoupling of the Dirac Hamiltonian. IV. Automated evaluation of molecular properties within the Douglas-Kroll-Hess theory up to arbitrary order. http://purl.org/coar/resource_type/c_6501