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Abstract Higher-order topological insulators have been introduced in the precursory Benalcazar-Bernevig-Hughes quadrupole model, but no electronic compound has been proposed to be a quadrupole topological insulator (QTI) yet. In this work, we predict that Ta2 M 3Te5 (M = Pd, Ni) monolayers can be 2D QTIs with second-order topology due to the double-band inversion. A time-reversal-invariant system with two mirror reflections (M x and M y ) can be classified by Stiefel-Whitney numbers (w 1, w 2) due to the combined symmetry T C 2z . Using the Wilson loop method, we compute w 1 = 0 and w 2 = 1 for Ta2Ni3Te5, indicating a QTI with q x y  = e/2. Thus, gapped edge states and localized corner states are obtained. By analyzing atomic band representations, we demonstrate that its unconventional nature with an essential band representation at an empty site, i.e., A g @4e, is due to the remarkable double-band inversion on Y–Γ. Then, we construct an eight-band quadrupole model with M x and M y successfully for electronic materials. These transition-metal compounds of A 2 M 1,3 X 5 (A = Ta, Nb; M = Pd, Ni; X = Se, Te) family provide a good platform for realizing the QTI and exploring the interplay between topology and interactions.