In this paper, we propose a mortar element method with Lagrange
multiplier for incompressible Stokes problem, i.e., the matching
constraints of velocity on mortar edges are expressed in terms of
Lagrange multipliers. We also present $P_1$ nonconforming element
attached to the subdomains. By proving inf-sup condition, we derive
optimal error estimates for velocity and pressure. Moreover, we
obtain satisfactory approximation for normal derivatives of the
velocity across the interfaces.