The single machine scheduling problem to minimize the number of tardy jobs is one of the most basic scheduling problems in scheduling theory. In 1973, Sidney studied the scheduling problem 1∣T∣∑Uj to minimize the number of tardy jobs with a subset T of the jobs which must be on time and give a polynomial time algorithm to solve this problem, the optimal could be gotten in time O(n log n). This algorithm is called Sidney Algorithm by scholars in the following years. In this paper, we revised Sidney Algorithm as following: Step1: Suppose E0＝T, J－E0＝{j1 , j2 , …, jm}, j1< j2<…< jm, m＝n－∣T∣, let k＝1; Step2: If k＝m+1, stop, then the schedule（Em，J－Em） is optimal; Else turn to step3; Step3: Arrange the jobs according to the earliest due date (EDD) schedule in Ek , assume Fk＝Ek-1∪{jk}, if Fk is a tardy subset, let Ek＝Ek-1∪{jk}; else Ek＝Fk\{jr},where the processing time of job jr satisfying: pr＝max{ pi∣ji?Fk\T }. Let k=k+1, turn to step2. In the end, we use induction to prove the schedule got from the revised algorithm is also an optimal solution for this problem.