  Millisecond pulsars, with magnetic fields weaker by three to four orders
compared to those of ordinary pulsars, are presumed to be neutron stars spun up
by binary accretion. We expect the magnetic field to get screened by the
accreted material. Our simulation of this screening mechanism shows, for the
first time, that the field decreases by a purely geometric factor $\sin^{-7/2}
\theta_{\rm P,i}$ before freezing to an asymptotic value, where $ \theta_{\rm
P,i}$ is the initial angular width of the polar cap. If $ \theta_{\rm P,i}$
lies in the range $5^o$--$10^o$, then the magnetic field diminution factor
turns out to be $\sim 10^3$--$10^4$ in conformity with observational data.
