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, KvW's 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 method's 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.