We present the algebraic solution to the Kepler problem - i.e. we show how to find all the possible trajectories of a testing body in the Newtonian gravitational field of a massive central body - without any need of integrating an equation of motion (differential equation). The presented idea is rather well-known on the scientific level, however, almost absolutely unknown in pedagogical level in spite of the fact it offers a nice possibility to explain the Keplerian elipses to the secondary school students.