Magnetic second-order topological insulator <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Cr</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mi>X</mml:mi> <mml:mi>Y</mml:mi> </mml:mrow> <mml:mo> </mml:mo> <mml:m

The realization of intrinsic second-order topological insulators (SOTIs) in two-dimensional magnetic systems has attracted considerable attention due to their unique physical properties and potential applications. The implementation of such materials fundamentally relies on nontrivial topological and magnetic orders. Although general design frameworks have been established through band engineering strategies, such as Zeeman field manipulation, the exploration of intrinsic magnetic SOTI systems still faces challenges. Followed by first-principles calculations, in this work, we report a series of intrinsic magnetic SOTIs ${\mathrm{Cr}}_{2}XY (X/Y=\mathrm{P},\mathrm{As},\mathrm{Sb})$ monolayers, which exhibit out-of-plane or in-plane intrinsic magnetic order and high Curie temperatures ($&gt;800\phantom{\rule{0.16em}{0ex}}\mathrm{K}$). Taking ${\mathrm{Cr}}_{2}{\mathrm{P}}_{2}$ and ${\mathrm{Cr}}_{2}{\mathrm{As}}_{2}$ monolayers as representative examples, we systematically reveal their second-order topological characteristics base on the Wannier functions of $p\text{\ensuremath{-}}d$ orbitals. We demonstrate floating edge states with second-order topology within the bulk gap and further elucidate topological characteristics using the nested Wilson loop method. Remarkably, corner-state substitution processes driven by discrete length modulation were observed in finite-sized nanoribbons. This provides a perspective for understanding the size effects of second-order topological corner states.