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Detailed monitoring of atmospheres of red supergiant stars is essential for the verification of physical models of mass loss. For such observations it is fundamentally important to employ methods resolving inhomogeneous stellar atmosphere. We present the observations of Betelgeuse using differential speckle polarimetry at the 2.5-m telescope of Caucasian Mountain Observatory of SAI MSU covering the period of 2019-2020 minimum. The observations were secured on 17 dates at wavelengths 465, 550, 625 and 880 nm. A circumstellar reflection nebula with the characteristic angular size of 0.1" was detected for all the dates and at all wavelengths. The morphology of the nebula changed significantly over the observational period. Net polarized brightness of the envelope remained constant until February 2020, while the stellar V band flux decreased 2.5 times. Starting from mid-February 2020, polarized flux of the envelope rose 2.1 times, at the same time the star returned to the pre-minimum state of October 2019.