The temperature course of the surface tension of supercooled water was suspected to exhibit an anomalous feature- the so-called second inflection point (SIP). Besides some theoretical and molecular simulation studies, this hypothesis was primarily supported by experimental data by P. T. Hacker [NACA TN 2510, 1951]. Recently, the present group performed accurate surface tension measurements down to -26 degrees C using a modified capillary rise [Hruby et al./. Phys. Chem. Lett 2014, 5, 425 and Vins et al. J. Phys. Chem. B 2015, 119, 5567] which, in contrast to Hacker's data, showed no SIP anomaly. To confirm that the qualitatively different observations are not related to some fundamental phenomenon, we developed an experimental device employing basically the same method as Hacker with a horizontal capillary tube. New experimental data for the surface tension of supercooled water measured with the horizontal capillary setup down to -23 degrees C are presented in this study. The new data show a very good agreement with the previous capillary rise measurements. It was confirmed that the temperature dependence of the surface tension is free of SIP in a temperature range from -23 to 23 degrees C and can be well-represented by the IAPWS standard extrapolated below 0.01 degrees C. However, a small systematic deviation from the IAPWS correlation can be seen at temperatures below -15 degrees C.