The magnetorotational instability (MRI) of a weakly ionized, differentially rotating, magnetized plasma disc is investigated in the multifluid framework. The disc is threaded by a uniform vertical magnetic field and charge is carried by electrons and ions only. The inclusion of ion inertia causes significant modification to the conductivity tensor in a weakly ionized disc. The parallel, Pedersen and Hall component of conductivity tensor becomes time-dependent quantities resulting in ac and dc components of the conductivity. The time dependence of the conductivity causes significant modification to the parameter window of MRI. The effect of ambipolar and Hall diffusion on the linear growth of the MRI is examined in the presence of time-dependent conductivity tensor. We find that the growth rate in the ambipolar regime can become somewhat larger than the rotational frequency, especially when the departure from ideal magnetohydrodynamics (MHD) is significant. Further, the instability operates on large scalelengths. This has important implication for angular momentum transport in the disc. When charged grains are the dominant ions, their inertia will play important role near the mid-plane of the protoplanetary discs. Ion inertia could also be important in transporting angular momentum in accretion discs around compact objects, in cataclysmic variables. For example, in cataclysmic variables, where mass flows from a companion main-sequence star on to a white dwarf, the ionization fraction in the disc can vary in a wide range. The ion inertial effect in such a disc could significantly modify the MRI and therefore this instability could be a possible driver of the observed turbulent motion.