  The pseudo-Finsleroid relativistic metric was constructed upon assuming that
the involved vector field $b_i$ is time-like. In the present paper it is shown
that the metric admits just the alternative counterpart in which the field is
space-like. The entailed pseudo-Finsleroid-spatial framework is systematically
described. We face on various remarkable properties, including the constant
curvature of the associated indicatrix, the explicit Hamiltonian function,
transparent presentations for the angle and scalar product. The spray
coefficients are found to be of a rather simple structure. The Berwald case is
attractively realized. Interesting conformal properties are stemming. {\bf
Keywords:} Finsler metrics, relativistic spaces, spray coefficients.
