We present the investigation of a monoclinic compound SeCuO3 using x-ray powder diffraction, magnetization, torque, and electron-spin-resonance. Structurally based analysis suggests that SeCuO3 can be considered as a three-dimensional network of tetramers. The values of intratetramer exchange interactions are extracted from the temperature dependence of the susceptibility and amount to similar to 200 K. The intertetramer coupling leads to the development of long-range antiferromagnetic order at T-N = 8 K. An unusual temperature dependence of the effective g tensors is observed, accompanied with a rotation of macroscopic magnetic axes. We explain this unique observation as due to site-selective quantum correlations.