We have analyzed the phase space distribution of a sample of about 900 non-kinematically selected low metallicity stars in the solar vicinity. The stars primarily represent the thick disk and halo populations of the Milky Way. We aim to identify overdensely populated regions in phase space, which we interpret as signatures of star streams passing close to the Sun. The search was conducted in a space constructed from the angular momenta and eccentricities of the stellar orbits. Besides recovering all well known star streams in the thick disk, we isolated four statistically significant phase space overdensities amongst halo stars. One of them is associated with a previously known halo star stream, but three of them are novel features, which we propose be also considered as genuine halo streams.