With high-resolution spectral observations using a 2.2-m telescope, we found that the Ap star BD+0°4535 has a very strong magnetic field. From Zeeman components of rare earth element spectral lines, we detected an average magnetic field modulus of about 21 kG, although for lines of different chemical elements the estimated magnetic field ranges between 15 and 23 kG. This is a consequence of non-uniform surface distribution of these elements. Considering its possible variation with rotation period, the upper limit of magnetic field is potentially larger than what we have detected. For rare earth elements, large overabundances and ionization disequilibria were found. © 2009 The Authors. Journal compilation © 2009 RAS.