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Magnetic moments of the A=12 unstable mirror pair nuclides 12B and 12N have been measured by the β-NMR technique. The experimentally measured magnetic moments are μ(12B)=1.001(17)μN and μ(12N)=0.4571(1)μN. The improved shell model using an SFO Hamiltonian with enhanced spin-isospin monopole proton-neutron interaction and modified single-particle energies is employed to calculate the magnetic moments of 12B and 12N. The calculation yields μ (12B)=0.929μN and μ(12N)=0.452μN and has produced a new magic number 6 for the short-lived unstable mirror pair nuclides 12B and 12N.