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We propose a modified split-cylinder resonator (SCR) with open slits, which can suppress the majority of TM modes while lowering the quality factors of nonzero azimuthal mode TE modes compared with grooves or protrusions. Thereby, the interference of unwanted modes on the TE<inline-formula> <tex-math notation="LaTeX">_{0n1}</tex-math> </inline-formula> measurements can be considerably reduced, which ultimately allows almost ten modes of TE<inline-formula> <tex-math notation="LaTeX">_{0n1}</tex-math> </inline-formula> (<inline-formula> <tex-math notation="LaTeX">n = 1</tex-math> </inline-formula>-10) to be used for excellent broadband and high-accuracy measurement. In addition, we newly derive a rigorous analysis of the SCR with the coaxial-type slits based on the mode matching method in detail, along with a joint iterative algorithm for considering simultaneously flange and slit. Then the numerical validation results suggest the accuracy and validity of the scheme over a wide range of dielectric sample thicknesses and slit widths. Finally, two cavities operating at 10-40 GHz and 20-78 GHz, respectively, were machined for experiments, and the improved SCR method is further validated by measuring several specimens processed from well-known materials, such as PTFE and several commercial substrates. The results demonstrate that the proposed method can perform broadband and high-accuracy measurement of the complex permittivity for dielectric samples of different thicknesses. In addition, the main sources of measurement uncertainty are also analyzed.