Space-borne nulling interferometers have long been considered as the best option for searching and characterizing extra-solar planets located in the habitable zone of their parent stars. Solutions for achieving deep starlight extinction are now numerous and well demonstrated. However they essentially aim at realizing an achromatic central null in order to extinguish the star. In this communication is described a major improvement of the technique, where the achromatization process is extended to the entire fringe pattern. Therefore higher Signal-to-noise ratios (SNR) and appreciable simplification of the detection system should result. The basic principle of this Fully achromatic nulling interferometer (FANI) consists in inserting dispersive elements along the arms of the interferometer. Herein this principle is explained and illustrated by a preliminary optical system design. The typical achievable performance and limitations are discussed and some initial tolerance requirements are also provided