Hardware-efficient implementation of sorting operation is crucial for numerous applications, particularly when fast and energy-efficient sorting of data is desired. Unary computing has been used for low-cost hardware sorting. This work proposes a comparison-free unary sorting engine by iteratively finding maximum values. Synthesis results show up to 81% reduction in hardware area compared to the state-of-the-art unary sorting design. By processing right-aligned unary bit-streams, our unary sorter is able to sort many inputs in fewer clock cycles.