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The surface tension of water is suspected to show a substantial increase at low temperatures, which is considered to be one of the many anomalies of water. The second inflection point (SIP) anomaly, originally claimed to be at around −8 °C, was experimentally refuted down to −25 °C by Hrubý et al. ( J. Phys. Chem. Lett. 2014, 5, 425–428). Recent molecular simulations predict the SIP anomaly near or even below the homogeneous freezing limit of around −38 °C. To contribute to an ongoing discussion about the SIP anomaly, new experiments focused on extreme levels of supercooling were carried out in this study. Unique experimental data down to −31.4 °C were collected using two measuring techniques based on the capillary rise method. A significant deviation from the extrapolated IAPWS formulation R1-76(2014) for surface tension of ordinary water was detected below −20 °C. Contrary to previous data, new experiments provide room for an anomaly in the course of surface tension in the deeply supercooled region.