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We succeeded in growing a GaN single crystal substrate with diameter of about two inches using the Na flux method. Our success is due to the development of a new apparatus for growing large GaN single crystals. The crystal grown in this study has a low dislocation density of 2.3×105 (cm-2), The secondary ion mass spectrometry (SIMS) technique demonstrates that the Na element is difficult to be taken in the crystal in both the + and – c directions, resulting in a Na concentration of 4.2 × 1014 (cm-3) in the crystal. Our success in growing a two-inch GaN substrate with a low impurity content and low dislocation density should pave the way for the Na flux method to become a practical application.