  We propose using matrix-isolated paramagnetic diatomic molecules to search
for the electric dipole moment of electron (eEDM). As was suggested by Shapiro
in 1968, the eEDM leads to a magnetization of a sample in the external electric
field. In a typical condensed matter experiment, the effective field on the
unpaired electron is of the same order of magnitude as the laboratory field,
typically about $10^{5}$V/cm. We exploit the fact that the effective electric
field inside heavy polar molecules is in the order of $10^{10}$V/cm. This leads
to a huge enhancement of the Shapiro effect. Statistical sensitivity of the
proposed experiment may allow one to improve the current limit on eEDM by three
orders of magnitude in few hours accumulation time.
