In modulo scheduling, the number of clock cycles between successive inputs (theinitiation interval, II) is tradi-tionally aninteger, but in this paper, we explore the benefitsof allowing it to be a rational number. This rational II canbe interpreted as theaveragenumber of clock cycles betweensuccessive inputs. As the minimum rational II can be less thanthe minimum integer II, this translates to higher throughput. We formulate rational-II modulo scheduling as an integer linear programming (ILP) problem that is able to find latency-optimal schedules for a fixed rational II. We have applied our scheduler to a standard benchmark of hardware designs, and our resultsdemonstrate a significant speedup compared to state-of-the-artinteger-II and rational-II formulations.