This paper presents a new methodology for model checking real-time systems based on the abstraction of time predicates. A real-time system is modeled with a timed automaton which is translated to a real-time program. The properties are specified with the temporal logic TCTL (Timed Computational Tree Logic). The real-time program and the TCTL property are used first, for producing a new automaton which augments the original with auxiliary clocks capturing the timing constraints in the TCTL specification that is reduced to an equivalent CTL specification. Second, the augmented real-time program is converted to a well timed system by removing the zeno runs (that are executions in which time does not diverge). Then the time predicates in the augmented automaton which is represented by an augmented and no-zeno real-time program will be abstracted to generate an untimed automaton representing an equivalent finite state system to be model checked using existing tools.