Unvegetated meandering rivers provide important analogues for pre-vegetation Earth and extraterrestrial landscapes. However, the factors governing their lateral migration remain insufficiently quantified. Prior research has suggested that migration rates of meandering rivers correlate with channel width, following a power law with an exponent of P = 0.85, with unvegetated channels migrating approximately 10 times faster than vegetated ones when measured at the bend apex. Here we present high-resolution data from six unvegetated dryland rivers, revealing a distinctive width-dependent pattern of lateral migration that we term "migration acceleration". The local power law exponent for migration as a function of width in narrow dryland reaches (4 m < W < 6 m) is 1.37, which smoothly increases to 2.29 for wider reaches (25 m < W < 40 m). Notably, the migration rates of narrow dryland streams align with those of vegetated streams from previous studies, while wide dryland streams exhibit migration rates comparable to unvegetated streams. Our findings show that the half-width-to-depth ratio of the reaches increases with channel width: narrow channels remain below the threshold for alternate bar formation, while wider channels exceed it. The presence of alternate bars in wide, unvegetated channels likely facilitates widening and accelerates migration-a process inhibited in vegetated streams by bank stabilization. We hypothesize that these higher migration rates result from weaker bank cohesion due to abiotic factors, which increase erosion susceptibility. These findings offer new insights into the dynamics of unvegetated meandering rivers and have significant implications for landscape evolution on Earth and extraterrestrial environments.