For 36 atoms from K to Xe, compact relativistic Gaussian-type function basis sets are developed in a segmented contraction form: (843(2)/74/7) for the third row atoms and (843(3)/743/74) for the fourth row atoms. Spin-free relativistic effects are considered through the third-order Douglas-Kroll approximation. The present basis sets are tested for all-electron calculations of four homo- and 12 heteronuclear diatomics in their ground states. The calculated spectroscopic constants are in good agreement with the experimental values. (C) 2009 Elsevier B.V. All rights reserved.