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We have shown that there is a specific kind of strongly localized surface plasmon modes that exist only on the periodically corrugated surface. These modes exist in the frequency range where the sum of the real parts of permittivities of metal and adjacent dielectric is positive. This frequency range is prohibited for conventional surface plasmon polaritons in the case of the flat metal surface. The reason why these modes arise is the surface-shape resonances [1] of single surface defect on flat surface. If such defects are periodically distributed on the surface than interaction among them leads to formation of nanoparticle chain waveguide [2, 3]. If the distance between defects is much smaller than free space wavelengths the eigenmodes of this chain waveguide are strongly localized. [1] P. C. Das and J. I. Gersten, Phys. Rev. B 25, 6281 (1982) [2] M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, Optics Letters, Vol. 23, №17, p. 1331 (1998) [3] D.G. Baranov, A.P. Vinogradov, A.A. Lisyansky, JOSA B, Vol.32, №2, p. 281 (2015)