%0 Journal Article %T Are rigid non-inertial frames of reference really rigid? %A S. S. Stepanov %J Physics %D 2013 %I arXiv %X In this paper the notion of the rigid frame of reference within special relativity is analysed. Three definitions of rigidity are formulated. By using several examples of non-inertial frames, it is shown that these definitions are not equivalent. It is also shown that so called M\"oller rigid non-inertial frames are locally rigid, but do not exhibit global rigidity. The physical meaning of this phenomenon is discussed, as well as its relation to the non-Euclidean nature of space in non-inertial frames of reference. (russian version) %U http://arxiv.org/abs/1306.4775v1