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

The Kwee - van Woerden (KvW) method for the determination of eclipse minimum times has been a staple in eclipsing binary research for decades, due its simplicity and independence of external input parameters, which makes it also well suited to obtain timings of exoplanet transits. However, its estimates of the timing error have been known to be of 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 way to calculate the timing error with the KvW method. A code that implements this improved method, together with several further updates over the original method is presented as well. An example application on the CM Draconis light curves from TESS is given, where we show that its timing errors of about 1 second are in excellent agreement with error estimates obtained by other means.