Detection of THz radiation by a high electron mobility (HEMT) GaAs/GaAlAs transistor was investigated at 4 K as a function of the magnetic field B. The detection signal (a source - drain photovoltage appearing as a response to THz radiation) was found to be periodic in B(exp -1), i.e., it showed Shubnikow - de Haas oscillations. A Fourier transform of the signal showed a large amplitude component independent of the gate polarization, and a small amplitude component dependent on it. This shows that a HEMT response to the radiation cannot be described either by a plasma instability in gated ("shallow water") or in ungated ("deep water") parts of the channel, but rather by a response of the channel as a whole. This is in a good correspondence with recent experimental evidence of antenna effects in detection of radiation by HEMTs and advanced theoretical models of instability of coupled gated - ungated plasma in HEMTs.