In this work we obtain a new description of the vertical motion of the car including the active suspension. It consists of 4 completely decoupled subsystems. The first 3 ones are of order 4 each and they are analogous to standard quarter suspension models. The 4 th subsystem is of order 2 and it introduces a new abstract variable denoted by γ. One of the novelties of this modeling result is that the full suspension system is no more seen as 4 decoupled quarter suspension models with sprung mass for each suspension being equal to a quarter of the total vehicle mass.