  It is pointed out that a cavity supernova (SN) explosion of a moving massive
star could result in a significant offset of the neutron star (NS) birth-place
from the geometrical centre of the supernova remnant (SNR). Therefore: a) the
high implied transverse velocities of a number of NSs (e.g. PSR B1610-50, PSR
B1757-24, SGR0525-66) could be reduced; b) the proper motion vector of a NS
should not necessarily point away from the geometrical centre of the associated
SNR; c) the circle of possible NS/SNR associations could be enlarged. An
observational test is discussed, which could allow to find the true
birth-places of NSs associated with middle-aged SNRs, and thereby to get more
reliable estimates of their transverse velocities.
