We present the results of the spectroscopic and photometric monitoring campaign of ASASSN-15ed. The transient was discovered quite young by the All Sky Automated Survey for SuperNovae (ASAS-SN). Amateur astronomers allowed us to sample the photometric SN evolution around maximum light, which we estimate to have occurred on JD = 2457087.4 +- 0.6 in the r-band. Its apparent r-band magnitude at maximum was r = 16.91 +- 0.10, providing an absolute magnitude M(r) ~ -20.04 +- 0.20, which is slightly more luminous than the typical magnitudes estimated for Type Ibn SNe. The post-peak evolution was well monitored, and the decline rate (being in most bands around 0.1 mag/d during the first 25 d after maximum) is marginally slower than the average decline rates of SNe Ibn during the same time interval. The object was initially classified as a Type Ibn SN because early-time spectra were characterized by a blue continuum with superimposed narrow P-Cygni lines of He I, suggesting the presence of a slowly moving (1200-1500 km/s), He-rich circumstellar medium. Later on, broad P-Cygni He I lines became prominent. The inferred velocities, as measured from the minimum of the broad absorption components, were between 6000 and 7000 km/s. As we attribute these broad features to the SN ejecta, this is the first time we have observed the transition of a Type Ibn SN to a Type Ib SN. ; Comment: 14 pages, 7 figures, 4 tables; published by MNRAS