Over the past decades, a number of methods have been proposed to handle cycle slips in the carrier phase measurements, but few researches have investigated receiver clock jumps, which may produce undesirable effects on GPS data processing. Such events are generally ignored in double-differenced positioning. For undifferenced processing, such as precise point positioning (PPP) techniques, it is unwise to neglect the impact of clock jumps. Failure to properly detect and account for receiver clock jumps may sometimes cause unexpected behavior of the GPS software and large errors in the resulting PPP solution. This is particularly troublesome when there are irregular (types 2 or 3) millisecond clock jumps represented in RINEX observation files. In this study, we first provide an intuitive description of the receiver clock jump phenomenon, and a comprehensive classification of clock jumps is presented according to its influence on three fundamental quantities (time tag, pseudorange, and carrier phase) of RINEX observation files. To follow the RINEX convention, the observable consistency is analyzed for various types of clock jump; and a simple but robust real-time clock jump compensation (RTCJC) method is proposed for reconstructing a consistent set of observables. Numerous validation tests with various GPS data show that the method is applicable to millisecond clock jumps. Without RTCJC, clock jumps are prone to cause failure of gross error and cycle slip detection algorithms and so result in repeated re-initialization or even non-convergent solutions, which lead to gross errors in the PPP solution. When RTCJC is applied, all clock jumps present in the GPS data can be effectively identified and repaired accurately, and the problem of re-initialization in PPP will no longer be triggered by receiver clock jumps, which results in significant improvement of PPP accuracy and reliability.