We introduce a simple single-band receiver clock jump and cycle slip (CJCS) detection and correction algorithm suitable for a standalone single-frequency Global Navigation Satellite System (GNSS) receiver. The real-time algorithm involves using an adaptive time differencing technique for the generation of adaptive differenced sequences of single-frequency code and phase observations. The sequences are used for determining thresholds and for the detection and determination of a receiver clock jump and cycle slips. The cycle slip values are fixed by rounding-up float values obtained via weighted least squares adjustment, following the elimination of the receiver's high-order clock drift at every epoch. The performance of this new technique was investigated with simulated cycle slip values and with different types of receiver clock jumps at millisecond and microsecond levels. It achieved 100% detection and correction of all types of receiver clock jumps; between 97 to 100% cycle slip detection; and between 96.9 to 100% cycle slip correction including cycle slips of ±1 cycle, for different rates of observations acquired by different fixed and mobile GNSS receivers. The algorithm thus facilitates precise timing and positioning on standalone low-cost single-frequency GNSS devices. unwanted frequent re-initializations, i.e., an overall reduced level of performance. Here, the authors present a new algorithm for dealing with this CJCS problem on a single-frequency GNSS receiver. Several single-frequency cycle slip correction methods, which are either code-phase based, phase-only based or doppler-inclusive based, exist. A code-phase method is presented in Fath-Allah (2010). This method is limited by the usual code-level errors that often prevent the detection of small cycle slip values. Phase-only methods found in Jia and Wu (2001) and Cosser et al. (2004) are based on 3rd-order differencing or fitting, which have no means of detecting and eliminating receiver clock jumps or achieving reliable detection of cycle slips in data sets with low observation rates. The Doppler-inclusive methods, such as found in Ren et al. (2011), combine Doppler measurements with phase and/or code observations. One drawback with the Doppler-inclusive technique is the inability to detect receiver clock jumps, plus the fact that not all single-frequency GNSS chip sets provide Doppler measurements. Known single-frequency techniques for addressing clock jumps are found in Momoh and Ziebart (2012), which involves phase differencing and code-based thresholding; and in Deo and El-Mowafy (2015), which is based on extrapolation and spline fitting of combined code and phase observations. These two methods are suitable for homogeneous clock jumps v J is at least half the number of satellites used in the clock jump detection, a clock jump is confirmed and its value, * J is computed as ** () v J mode J (12) where mode is the arithmetic mode operator. Outliers, if any, are excluded from the values in * v J before the mode value is computed. There is no cloc...