Assuming the existence of an invariant velocity a slightly generalized form of Lorentz transformations is derived. The group of these transformations has a simpler composition law than the group of standard Lorentz transformations has. It is shown that this new form allows the description of both subluminal and superluminal motions. It also allows to find all velocity-dependent tensors. In particular, the tachyonic momentum as a function of superluminal velocity is derived.
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