Electronic band structures is a cornerstone of condensed matter physics and materials science. Conventional methods like Wannier interpolation (WI), which are commonly used to interpolate band structures onto dense k-point grids, often encounter difficulties with complex systems, such as those involving entangled bands or topological obstructions. In this work, we introduce the Hamiltonian transformation (HT) method, a novel framework that directly enhances interpolation accuracy by localizing the Hamiltonian. Using a pre-optimized transformation, HT produces a far more localized Hamiltonian than WI, achieving up to two orders of magnitude greater accuracy for entangled bands. Although HT utilizes a slightly larger, nonlocal numerical basis set, its construction is rapid and requires no optimization, resulting in significant computational speedups. These features make HT a more precise, efficient, and robust alternative to WI for band structure interpolation, as further verified by high-throughput calculations.