$k$-nearest neighbour ($k$-NN) is one of the simplest and most widely-used\nmethods for supervised classification, that predicts a query's label by taking\nweighted ratio of observed labels of $k$ objects nearest to the query. The\nweights and the parameter $k \\in \\mathbb{N}$ regulate its bias-variance\ntrade-off, and the trade-off implicitly affects the convergence rate of the\nexcess risk for the $k$-NN classifier; several existing studies considered\nselecting optimal $k$ and weights to obtain faster convergence rate. Whereas\n$k$-NN with non-negative weights has been developed widely, it was also proved\nthat negative weights are essential for eradicating the bias terms and\nattaining optimal convergence rate. In this paper, we propose a novel\nmultiscale $k$-NN (MS-$k$-NN), that extrapolates unweighted $k$-NN estimators\nfrom several $k \\ge 1$ values to $k=0$, thus giving an imaginary 0-NN\nestimator. Our method implicitly computes optimal real-valued weights that are\nadaptive to the query and its neighbour points. We theoretically prove that the\nMS-$k$-NN attains the improved rate, which coincides with the existing optimal\nrate under some conditions.\n