  Keeping the two fundamental postulates of the special theory of relativity,
the principle of relativity and the constancy of the one-way velocity of light
in all inertial frames of reference, and assuming two generalized Finslerian
structures of gravity-free space and time in the usual inertial coordinate
system, we can modify the special theory of relativity. The modified theory is
still characterized by the localized Lorentz transformation between any two
usual inertial coordinate systems. It together with the quantum mechanics
theory features a convergent and invariant quantum field theory. The modified
theory also involves a new velocity distribution for free particles that is
different from the Maxwell distribution. It is claimed that the deviation of
the new distribution from its previous formula will provide experimental means
of judging the modified special relativity theory.
