We present in this paper, the first results of a spectropolarimetric analysis of a small sample (~20) of active stars ranging from spectral type M0 to M8, which are either fully convective or possess a very small radiative core. This study aims at providing new constraints on dynamo processes in fully convective stars. This paper focuses on ve stars of spectral type ~M4, i.e. with masses close to the full convection threshold (0.35M_{sun}_), and with short rotational periods. Tomographic imaging techniques allow us to reconstruct the surface magnetic topologies from the rotationally modulated time-series of circularly polarized profiles. We find that all stars host mainly axisymmetric large-scale poloidal fields. Three stars were observed at two different epochs separated by 1yr; we find the magnetic topologies to be globally stable on this time-scale. We also provide an accurate estimation of the rotational period of all stars, thus allowing us to start studying how rotation impacts the large-scale magnetic field.