An experimental study for the unbound nucleus 13Be has been performed by means of the invariant mass method via the one-neutron removal reaction 1H (14Be, 12Be + n). A resonance has been observed at 0.51(1) MeV in the relative energy (Erel) spectrum of the 12Be + n system. The transverse momentum distribution of the 12Be + n system as well as the resonance width of 0.45(3) MeV gives evidence for the p-wave nature of the resonance. A d-wave resonance has also been observed at 2.39(5) MeV in the Erel spectrum. The observation of the low-lying p-wave resonance indicates the disappearance of the N = 8 magicity in the vicinity of the neutron drip line region. © 2010 Elsevier B.V. All rights reserved.