  We report on a new evolutionary path leading to the formation of close double
neutron stars (NS), with the unique characteristic that none of the two NS ever
had the chance to be recycled by accretion. The existence of this channel stems
from the evolution of helium-rich stars (cores of massive NS progenitors),
which has been neglected in most previous studies of double compact object
formation. We find that these non-recycled NS-NS binaries are formed from bare
carbon-oxygen cores in tight orbits, with formation rates comparable to or
maybe even higher than those of recycled NS-NS binaries. On the other hand,
their detection probability as binary pulsars is greatly reduced (by about
1000) relative to recycled pulsars, because of their short lifetimes. We
conclude that, in the context of gravitational-wave detection of NS-NS inspiral
events, this new type of binaries calls for an increase of the rate estimates
derived from the observed NS-NS with recycled pulsars, typically by factors of
1.5-3 or even higher.
