For high cycle fatigue simulations, cyclic loads are often replaced by constant envelope loads using a cycle jump technique. However, this simplification cannot be used under general loading conditions where the local stress ratios can substantially deviate from global load ratios. The local stress ratios have to be determined for every material point individually by periodically performing a full loadingunloading cycle. Usually, commercial finite element (FE) solvers use time integration methods that are not energy-conserving, so that the simulation of such a loading-unloading cycle produces a numerical energy error. In this contribution, a new cycle jump and load application technique for high cycle fatigue simulations under general loading conditions is presented. It combines the simulation of full load cycles to determine local stress ratios with cycle jumps to save computational costs. The new technique is characterized by its energy-conserving behavior which is reached by a complete unloading of the FE model after each cycle jump and a modified formulation of the element residual vectors. By using userdefined elements, this modified formulation can also be used with commercial FE solvers.