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Accurate propagation characteristics are essential for future indoor millimeter-wave (mmWave) small cell network planning. This paper presents propagation measurements at 26 GHz and 38 GHz which are important candidate bands for fifth generation mmWave communication. Measurements are conducted in an indoor corridor, as well as a stairwell whose mmWave channel is seldom investigated before. In these measurements, an omnidirectional biconical antenna is used as transmitter and a steerable directional horn antenna is used as receiver. The directional and omnidirectional path loss exponents, shadow factors, cross-polarization discrimination ratios and root-mean-square delay spreads are analyzed for both line-of-sight and non-line-of-sight scenarios in both co-polarization and cross-polarization, and these characteristics are compared for different frequencies and environments. It is found obvious depolarization phenomenon in non-line-of-sight scenario for higher frequency. Compared to the corridor, the stairwell has larger path loss exponents and root-mean-square delay spreads, and the depolarization is also more evident in stairwell. The results in this paper are beneficial to building efficient and robust indoor mmWave communication systems.