High-resolution thermal-expansion measurements of single-crystalline CuO (tenorite) are reported for the temperature range 5 < T < 350 K. The data reveal three transitions (T N1 = 213 K, T N2 = 229.2 K, and T N3 = 229.8 K), which corroborate the recently proposed magnetic phase diagram [Villarreal, Quirion, Plumer, Poirier, Usui, and Kimura, Phys. Rev. Lett. 109, 167206 (2012)] revealing three distinct antiferromagnetic (AFM) phases. Analysis of the region surrounding T N2 and T N3 suggests that these phase transitions are continuous and yields estimates for the heat-capacity critical exponents of α T N2 = 0.033(2) and α T N3 = 0.040(9). Magnetic susceptibility measurements reveal spin-flop transitions at temperatures below T N1 , confirming that the b axis is the easy AFM axis.