|We propose 8.4 and 15 GHz phase-referenced observations to investigate whether a central component in the composite supernova 1986J is indeed a pulsar nebula. We will make a spectral index map and identify the component that causes the high-frequency inverted spectrum of the supernova. We will determine with astrometry whether it is indeed stationary as expected and locate it relative to the geometric center of the shell. This is the the best chance so far of lurking a pulsar nebula lurking in the debris of a supernova explosion. These observations complement our earlier 5-GHz observations. The increased resolution will aid in exposing more clearly the hot spots and possible short jets emanating from the remnant of the explosion. Characteristics of this supernova may have links to those of gamma ray bursters.