In this paper, we present new and archive radio measurements obtained with the Very Large Array of the magnetic chemically peculiar (MCP) star Orionis E. The radio data have been obtained at different frequencies and they are well distributed along the rotational phases. We analyse in detail the radio emission from Ori E with the aim of finding evidence for circularly polarized radio pulses. Up to now, among MCP stars, only CU Virginis has shown 100 per cent polarized time-stable radio pulses, explained as highly directive electron cyclotron maser emission, visible from Earth at particular rotational phases, like a pulsar. Our analysis shows that there is no hint of coherent emission at frequencies below 15 GHz. We conclude that the presence of a quadrupolar component of the magnetic field, dominant within few stellar radii from the star, where the maser emission should be generated, inhibits the onset of the cyclotron maser instability in Ori E.