We present 21-cm line observations of the spiral galaxy NGC4559, made with the Westerbork Synthesis Radio Telescope. We have used them to study the HI distribution and kinematics, the relative amount and distribution of luminous and dark matter in this galaxy and, in particular, the presence of extra-planar gas. Our data do reveal the presence of such a component, in the form of a thick disk, with a mass of 5.9 x 10(8) M-circle dot (one tenth of the total HI mass) and a mean rotation velocity 25-50 km s(-1) lower than that of the thin disk. The extra-planar gas may be the result of galactic fountains but accretion from the IGM cannot be ruled out. With this study we confirm that lagging, thick HI layers are likely to be common in spiral galaxies.