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The Kwee - van Woerden (KvW) method used for the determination of eclipseminimum times has been a staple in eclipsing binary research for decades, dueits simplicity and the independence of external input parameters, which alsomakes it well-suited to obtaining timings of exoplanet transits. However, itsestimates of the timing error have been known to have a low reliability. Duringthe analysis of very precise photometry of CM Draconis eclipses from TESS spacemission data, KvW's original equation for the timing error estimate producednumerical errors, which evidenced a fundamental problem in this equation. Thiscontribution introduces an improved approach for calculating the timing errorwith the KvW method. A code that implements this improved method, together withseveral further updates of the original method, are presented. An example ofthe application to CM Draconis light curves from TESS is given. The eclipseminimum times are derived with the KvW method's three original light curvefolds, but also with five and seven folds. The use of five or more foldsproduces minimum timings with a substantially better precision. The improvedmethod of error calculation delivers consistent timing errors which are inexcellent agreement with error estimates obtained by other means. In the caseof TESS data from CM Draconis, minimum times with an average precision of 1.1seconds are obtained. Reliable timing errors are also a valuable indicator forevaluating if a given scatter in an O-C diagram is caused by measurement errorsor by a physical period variation.

A modified Kwee - van Woerden method for eclipse minimum timing with reliable error estimates