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The absolute branching fraction of the decay Λc(2625)+→Λ+cπ+π− is measured for the first time to be (50.7±5.0stat.±4.9syst.)% with 368.48 pb−1 of e+e− collision data collected by the BESIII detector at the center-of-mass energies of s√=4.918 and 4.950 GeV. This result is lower than the naive prediction of 67\%, obtained from isospin symmetry, by more than 2σ, thereby indicating that the novel mechanism referred to as the \textit{threshold effect}, proposed for the strong decays of Λc(2595)+, also applies to Λc(2625)+. This measurement is necessary to obtain the coupling constants for the transitions between s-wave and p-wave charmed baryons in heavy hadron chiral perturbation theory. In addition, we search for the decay Λc(2595)+→Λ+cπ+π−. No significant signal is observed, and the upper limit on its branching fraction is determined to be 80.8\% at the 90\% confidence level.