We have used the LOw-Frequency ARray (LOFAR) to search for the growing tip of an intra-cloud (IC) positive leader. Even with our most sensitive beamforming method, where we coherently add the signals of about 170 antenna pairs, we were not able to detect any emission from the tip. Instead, we put constraints on the emissivity of very-high frequency (VHF) radiation from the tip at 0.5 pJ/MHz at 60 MHz, integrated over 100 ns. The limit is independent on whether this emission is in the form of short pulses or continuously. We conclude that IC positive leaders propagate in a continuous process which is in sharp contrast to what is seen to the step-wise propagation seen in some cloud-to-ground positive leaders and for all negative leaders.