  The fraction of long duration gamma ray bursts (GRBs) without an associated
bright supernovae (SNe) at small redshifts $(z<0.15)$ is comparable to that of
GRBs associated with SNe. We show, that their X-ray afterglow and the X-ray
afterglow of most of the nearby $(z<1)$ GRBs without a confirmed association
with SNe, are well reproduced by the launch of highly relativistic jets in the
SN-less birth of millisecond pulsars in neutron star mergers or through phase
transition of neutron stars to quark stars following mass accretion in compact
binaries. Such a large fraction of GRBs with pulsar-like afterglow that extends
to very large redshifts $(z>4)$, however, favors phase transition of neutron
stars to quark stars in high mass X-ray binaries (HMXBs), rather than merger of
neutron stars, as the origin of SN-less GRBs.
