  In the present study, we have derived the Lorentz factor using a coordinate
system with antiparallel X-axes. Using a thought experiment, common in
relativistic literature, we have used the case of a pulse of light moving along
the X-axis. Next, we have argued that, consequently with the isotropy of space,
the result must be the same if the trajectory of the light pulse is any angle
$\alpha>0^{\circ}$, thus obtaining an alternative transformation factor that
generates the same results as the Lorenz factor at any angle of the trajectory
of the light pulse, therefore confirming the relativistic isotropy of space in
the context of the Minkowski spacetime. Nevertheless, a particularly important
novelty is that the derived alternative transformation factor allows the
reference frames involved to move at speeds greater than that of light.
