The recent TAU computer-aided design (CAD) contest has aimed to seek novel ideas for accurate and fast clock network pessimism removal (CNPR). Unnecessary pessimism forces the static-timing analysis (STA) tool to report worse violation than the true timing properties owned by physical circuits, thereby misleading signoff timing into a lower clock frequency at which circuits can operate than actual silicon implementations. Therefore, we introduce in this paper UI-Timer, a powerful CNPR algorithm which achieves exact accuracy and ultra-fast runtime. Unlike existing approaches which are dominated by explicit path search, UI-Timer proves that by implicit path representation the amount of search effort can be significantly reduced. Our timer is superior in both space and time saving, from which memory storage and important timing quantities are available in constant space and constant time per path during the search. Experimental results on industrial benchmarks released from TAU 2014 CAD contest have justified that UI-Timer achieved the best result in terms of accuracy and runtime over all participating timers.