[en] Magnetic properties of single crystal Ba₂Cu₃O₄Cl₂ with Cu₃O₄ planes were investigated by temperature- and magnetic-field-dependent anisotropic magnetization M(T,H) and zero-field-μSR. Muon spin precession was observed below as well as above T=32 K where an anomaly in M(T) appears. At this temperature the frequency of the precession changes and the damping of it diverges. This is an evidence for a magnetic transition. We also found the temperature dependence of the H-linear component of M(H) shows a maximum around T=80 K, which is similar to the behavior of low-dimensional magnets with an antiferromagnetic interaction