The invention relates to a pipetting system which includes two base structures: a pipetting base, with most of the components and subsystems of known pipetting systems, and a coupling base, which adds novel subsystems to the unit. Since the two bases can be coupled together, various modes and variations are derived therefrom, since a large number of configurations and architectures can be conceived of, in accordance with the level in which it is defined (1 to 3). In particular, an insertion/ejection subsystem is provided, which makes it highly efficient to replace disposable tips, which is carried out in two ways: with the nozzle moving towards the disposable tip or vice-versa (with the nozzle stationary). Examples of manual pipetting systems are shown for each case. The invention includes the mode of having a box with new and used disposable tips, for recycling the plastic. The pipetting system can be used both in the manual case and in the automatic case, having advantages in both cases over current systems, and a method which also applies to both cases is established.