We consider the boundary-value problem for the steady isothermal flow of an incompressible viscoelastic liquid of
Oldroyd type in a bounded domain with a Navier type slip boundary condition. We prove that under some restrictions on
the material constants and the data, there exists a strong solution which is locally unique. The proof is based on a fixed
point argument in which the boundary-value problem is decomposed into a transport equation and a Stokes system.