In most GPS (Global Positioning System) receivers, the pseudo-range measurement error is bigger than the wavelength of WL (Wide Lane) carrier phase measurement. It will probably cause one cycle WL integer ambiguity resolution error in case the DD (Double Differenced) WL integer ambiguity is rounded by DD pseudo-range measurement according to the WL integer bootstrapping model. In this view of, we propose a modified WL bootstrapping ambiguity resolution algorithm. The proposed algorithm mainly aims at detecting and repairing one cycle WL integer ambiguity error. The WL integer ambiguity error detector is designed according to the characteristic that the integer ambiguity is an integer. The designed detector is compared with the theoretical threshold calculated by the Carrier Noise Ratio (CNR) to judge whether the WL integer ambiguity is wrong. There are only 3 degrees of freedom in all the ambiguities, therefore we fix the wrong ambiguities by the right ambiguities. We analyze the feasibility of the proposed algorithm in Gaussian noise environment. The results show all the carrier phase measurement in normal CNR environment can judge whether the WL integer ambiguity has one cycle error. The maximum carrier phase error is calculated in case we consider the multipath and other carrier phase measurement error. The probability of one cycle WL integer ambiguity error is analyzed with pseudo-range measurement error in different orders of magnitude. Field tests were carried out by using GPS short baseline data. The proposed algorithm increases the success rate of the WL integer bootstrapping ambiguity resolution algorithm from less than 1/3 to nearly 100%.