This paper presents a QR update implementation of the successive column correction (SCC) method and a column-secant modification of the SCC method, which is called the CSSCC method. The computational cost of the QR update technique for the SCC method is much less than that for Broyden's method. The CSSCC method uses function values more efficiently than the SCC method, and it shown that the CSSCC method has better local q-convergence and r-convergence rates than the SCC method. The numerical results show that the SCC method and the CSSCC method with the QR update technique are competitive with some well known methods for some standard test problems.