  Recently, extra motivation has been given to the investigations of an
unresolved problem of millisecond pulsars (MSPs) produced by the recycling
process, as an apparent role of the accretion-induced collapse (AIC) in white
dwarfs (WDs) was suggested to this concern. I have found that the distribution
of the orbital periods of binary MSPs in the Galactic disk closely follows an
exponential distribution. I have also determined the best-fit mean value of
Nobs by fitting our data with an exponential distribution for the MSP
population. As a result, it can be stated that reaching the Chandrasekhar limit
may cause an explosion of a massive WD as a Type Ia supernova (in the case of a
CO WD) or an ignition of a ONeMg WD, and possibly merging in some CO WDs, all
resulting in peculiar MSP systems. A possible formation scenario, where the
system has a circular orbit during this evolutionary stage, is discussed.
