Abstract. The X-ray absorption spectra around the Cr K-edge are observed to reveal the strange behaviour on the magnetism of the dilute magnetic semiconductor GaCrN with a cubic structure (F3 m = Td²). The radial distribution function analyzed in the part of the X-ray absorption fine structure shows the splitting in the first and the second nearest neighbours into two peaks, indicating that the Cr ion substitutes the Ga ion but shifts from just the lattice site of the Ga ion. This local lattice instability breaking the symmetry is explained by pseudo-Jahn – Teller effect. In the relation to the local lattice instability, the electronic ground state of the Cr ion in the cubic GaN is discussed.