We present the results of deep radio observations with the Australia Telescope Compact Array (ATCA) of the globular cluster NGC 6388. We show that there is no radio source detected (with a r.m.s. noise level of 27 uJy) at the cluster centre of gravity or at the locations of the any of the Chandra X-ray sources in the cluster. Based on the fundamental plane of accreting black holes which is a relationship between X-ray luminosity, radio luminosity and black hole mass, we place an upper limit of 1500 M_sun on the mass of the putative intermediate-mass black hole located at the centre of NGC 6388. We discuss the uncertainties of this upper limit and the previously suggested black hole mass of 5700 M_sun based on surface density profile analysis.
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