Bottleneck Assignment Problem has already been solved by Gross [5], Gar-Finkel [3] and Bhatia [1]. Starting with an assignment yielding minimum completion time, the present paper presents two procedures for ranking various assignments in order of increasing completion time. In the first, closed circuits satisfying certain conditions are found. Non-existence of such circuits at a particular time imply no assignment yielding that completion time. In the second procedure a cost minimizing assignment problem is solved to get an assignment yielding next best time, Murty's [8] cost ranking procedure has been suitably modified for time ranking and is discussed in a note in this paper.