Identifying axial vectors and pseudoscalars as antisymmetric 3-component and 4-component tensors in space-time of arbitrary dimensions, we discover a new PCAC law: ∂[Kψ¯ΓLΓMΓN]=\partial [_{K\bar \psi } \Gamma _L \Gamma _M \Gamma _{N]} = =2miψ¯Γ[KΓLΓM