Semi-partitioned scheduling is a new approach for allocating tasks on multiprocessor platforms. By splitting some tasks between processors, semi-partitioned scheduling is used to improve processor utilization. In this paper, a new semi-partitioned scheduling algorithm called SS-DRM is proposed for multiprocessor platforms. The scheduling policy used in SS-DRM is based on the delayed rate monotonic algorithm, which is a modified version of the rate monotonic algorithm that can achieve higher processor utilization. This algorithm can safely schedule any system composed of two tasks with total utilization less than or equal to that on a single processor. First, it is formally proven that any task which is feasible under the rate monotonic algorithm will be feasible under the delayed rate monotonic algorithm as well. Then, the existing allocation method is extended to the delayed rate monotonic algorithm. After that, two improvements are proposed to achieve more processor utilization with the SS-DRM algorithm than with the rate monotonic algorithm. According to the simulation results, SS-DRM improves the scheduling performance compared with previous work in terms of processor utilization, the number of required processors, and the number of created subtasks.