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We prove the structural result on normal plane maps, which applies to the vertex distance colouring of plane maps. The vertex distance-t chromatic number of a plane graph G with maximum degree Δ(G) ≤ D, D ≥ 12 is proved to be upper bounded by $6+[(2D+12)/(D-2)]({(D-1)}^{(t-1)}-1)$. This improves a recent bound $6+[(3D+3)/(D-2)]({(D-1)}^{t-1}-1)$, D ≥ 8 by Jendrol’ and Skupień, and the upper bound for distance-2 chromatic number.