AN important clue to the nature of soft gamma-ray repeaters (SGRs), wh
ich emit recurrent bursts of gamma-rays, has been provided by the asso
ciation of two of the three known SGRs with supernova remnants(1,2) (S
NRs). Here we present radio images of the nonthermal radio nebula G10.
0-0.3, a supernova remnant which has been associated previously(2) wit
h SGR1806-20 (refs 3, 4). Our images show that the nebula is a plerion
(that is, the radio emission is synchrotron radiation powered by a ce
ntral pulsar), as revealed by the observation of a hierarchy of nested
shells and a bright central peak. The recent detection(5) of an X-ray
point source coincident with the radio peak and of a hard X-ray burst
(5,6) from G10.0-0.3 confirms the SGR-SNR association. We propose that
SGR1806-20 is an isolated pulsar that emits both steady and impulsive
winds of relativistic particles, which together power the nebula. We
suggest that the offset from the centres of the SNRs observed for both
this object and SGR0526-66 (ref. 1), requiring high velocities of the
pulsars, provides a clue to their formation mechanism.