The work focuses upon the relativistic and geometric properties of the
space--time endowed tentatively with the metric function of the Berwald--Moor
type. The zero curvature of indicatrix is a remarkable property of the
approach. We demonstrate how the associated geodesic equations can be solved in
a transparent way, thereby obtaining possibility to introduce unambiguously the
distance, angle, and scalar product. We find convenient indicatrix
representation for the associated tetrads and, by attributing to them naturally
the general meaning of the bases proper of inertial reference frames, elucidate
respective fundamental kinematic relations, including the extensions of Lorentz
transformations and velocity subtraction and composition laws. The invariance
group for the metric tensor is found.