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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 Ta2M3Te5 (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 (Mx and My) can be classified by Stiefel-Whitney numbers (w1, w2) due to the combined symmetry TC2z. Using the Wilson loop method, we compute w1 = 0 and w2 = 1 for Ta2Ni3Te5, indicating a QTI with qxy = 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., Ag@4e, is due to the remarkable double-band inversion on Y–Γ. Then, we construct an eight-band quadrupole model with Mx and My successfully for electronic materials. These transition-metal compounds of A2M1,3X5 (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.