We study the basic features of the two-dimensional quantum Hubbard Model at half-filling by means of the Lüscher algorithm and the algorithm based on direct update of the determinant of the fermionic matrix. We implement the Lüscher idea employing the transfer matrix formalism which allows to formulate the problem on the lattice in (2+1) dimensions. We discuss the numerical complexity of the Lüscher technique, systematic errors introduced by polynomial approximation and introduce some improvements which reduce long autocorrelations. In particular we show that preconditioning of the fermionic matrix speeds up the algorithm and extends the available range of parameters. We investigate the magnetic and the one-particle properties of the Hubbard Model at half-filling and show that they are in qualitative