We present precise values of the eccentricity and periastron angle of 529 detached, eccentric, eclipsing stars from the Kepler Eclipsing Binary catalog that were determined by modeling their long cadence data. The temperatures and relative radii of their components as well as their mass ratios were calculated based on approximate values of the empirical relations of MS stars. Around one-third of the secondary components were revealed to be very late dwarfs, some of them possible brown dwarf candidates. Most of our targets fall below the envelope P(1-e^2^)^3/2^=5days. The (e,P) distribution of the known eccentric binaries exhibits a rough trend of increasing eccentricity with the period. The prolonged and continuous Kepler observations allowed us to identify 60 new highly eccentric targets with e>0.5.