The Kwee - van Woerden (KvW) method used for the determination of eclipse minimum times has been a staple in eclipsing binary research for decades, due its simplicity and the independence of external input parameters, which also makes it well-suited to obtaining timings of exoplanet transits. However, its estimates of the timing error have been known to have a low reliability. During the analysis of very precise photometry of CM Draconis eclipses from TESS space mission data, KvWs original equation for the timing error estimate produced numerical errors, which evidenced a fundamental problem in this equation. This contribution introduces an improved approach for calculating the timing error with the KvW method. A code that implements this improved method, together with several further updates of the original method, are presented. An example of the application to CM Draconis light curves from TESS is given. The eclipse minimum times are derived with the KvW methods three original light curve folds, but also with five and seven folds. The use of five or more folds produces minimum timings with a substantially better precision. The improved method of error calculation delivers consistent timing errors which are in excellent agreement with error estimates obtained by other means. In the case of TESS data from CM Draconis, minimum times with an average precision of 1.1 seconds are obtained. Reliable timing errors are also a valuable indicator for evaluating if a given scatter in an O-C diagram is caused by measurement errors or by a physical period variation.
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