For the search for additional Higgs bosons in the Minimal Supersymmetric Standard Model (MSSM) as well as for future precision analyses in the Higgs sector a precise knowledge of their decay properties is mandatory. We evaluate all two-body decay modes of the heavy Higgs bosons into sfermions in the MSSM with complex parameters (cMSSM). The evaluation is based on a full one-loop calculation of all decay channels, also including hard QED and QCD radiation. The dependence of the heavy Higgs bosons on the relevant cMSSM parameters is analyzed numerically. We find sizable contributions to many partial decay widths. They are roughly of O(15%) of the tree-level results, but can go up to 30% or higher. The size of the electroweak one-loop corrections can be as large as the QCD corrections. The full one-loop contributions are important for the correct interpretation of heavy Higgs-boson search results at the LHC and, if kinematically allowed, at a future linear e+e- collider. The evaluation of the branching ratios of the heavy Higgs bosons will be implemented into the Fortran code FeynHiggs.