Reciprocity Independent Lorentz Transformation
  We have defined slowness (or reciprocal velocity, corresponding to velocity v) as cc/v, where c is the speed of light. It is observed that the relative velocity remains invariant if the velocities are replaced by corresponding slownesses i.e. relative motion in one dimension is reciprocal symmetric. Reciprocity operation, which converts a velocity to the corresponding slowness, is found. Lorentz transformation is generalized so that Lorentz invariance is maintained if velocities are replaced by corresponding slownesses. 
Mushfiq Ahmad