We present the results of a second epoch of 18‐cm global very long baseline interferometry (VLBI) observations, taken on 2001 February 23, of the central kiloparsec of the nearby starburst galaxy Messier 82. These observations further investigate the structural and flux evolution of the most compact radio sources in the central region of M82. The two most compact radio objects in M82 have been investigated (41.95+575 and 43.31+592). Using this recent epoch of data in comparison with our previous global VLBI observations and two earlier epochs of European VLBI network observations, we measure expansion velocities in the range of 1500–2000 km s−1 for 41.95+575 and 9000–11 000 km s−1 for 43.31+592 using various independent methods. In each case, the measured remnant expansion velocities are significantly larger than the canonical expansion velocity (500 km s−1) of supernova remnants (SNRs) within M82 predicted from theoretical models. In this paper, we discuss the implications of these measured expansion velocities with respect to the high‐density environment that the SNRs are expected to reside in within the centre of the M82 starburst.