The search for and understanding of low-dimensional magnetic materials is essential for both fundamental and technological purposes. Here we propose a combined experimental and theoretical investigation of such a system, namely the monoclinic phase of SeCuO3. This low-dimensional spin-1/2 antiferromagnet appears to be based on two decoupled magnetic subsystems which respond differently to applied magnetic field in the antiferromagnetic phase. From our results we are able to propose a zero-field magnetic structure as well as a more exotic finite magnetic field structure, to be tested by future experiments. This finding is based on torque magnetometry measurements on the one side, and the use of a refined phenomenological model and state-of-the-art density functional theory calculations on the other. The existence of such systems opens a way to very exciting physics with the possibility to control separately two magnetic subsystems in one material.