The authors consider a movement of a classical particle in a plane with periodic lattice of inpenetrable line-segments parallel to one edge of a square elementary cell and half of its width. Such a pseudo-integrable system takes intermediate place between integrable and ergodic ones. A particle movement in the billiard is thoroughly analysed and expressed in terms of a continued fraction for a trajectory gradient. Rational gradients are shown to correspond to periodic orbits. Quadratic irrational gradients lead to power law correlation decay with calculable fractal dimensions. For generic irrational gradients the numerical investigations are presented.