Finslerian extension of Lorentz transformations

F-rotations which leave Finslerian metric functions invariant are derived systematically. They extend ordinary Lorentz transformations or pseudo-Riemannian rotations to the Finslerian approach. Explicit representations for F-rotations covering the future-time-like, space-like, past-time-like, or isotropic sectors can be obtained. The invariant metric tensors and fundamental frame fields are also found. Convenient forms for extended Lorentz transformations are derived.