  We present an evolutionary scenario for the spin-up and evolution of binary
millisecond pulsars, according to which the companion of the pulsar PSR J
1740-5340, recently discovered as a binary with orbital period of 32.5 hr in
the Globular Cluster NGC 6397, is presently in a phase of ``radio-ejection''
mass loss from the system. At present, Roche lobe overflow due to the nuclear
evolution of the pulsar companion and to systemic angular momentum losses by
magnetic braking is still going on, but accretion is inhibited by the momentum
exerted by the radiation of the pulsar on the matter at the inner Lagrangian
point. The presence of this matter around the system is consistent with the
long lasting irregular radio eclipses seen in the system. Roche lobe
deformation of the mass losing component is also necessary to be compatible
with the optical light curve. The "radio-ejection" phase had been recently
postulated by us to deal with the problem of the lack of submillisecond pulsars
(Burderi et al. 2001, ApJ, 560, L71).
