[en] The self-consistent one-electron wave functions and energy bands obtained by the LMTO-ASA method within the local density approximation (LDA) are used to calculate the wave vector and frequency dependent non-interacting spin susceptibility of parmagnetic La₂CuO₄ in the body-centered tetragonal (bct) structure. In this paper, the authors show that the tendency towards the antiferromagnetic instability is strongly dependent on the effects of the matrix elements which lead to a substantial depression of the susceptibility, especially near the X-point. The Fermi surface nesting properties, although important for the susceptibility, are by far not sufficient for the instability and the interband transitions turn out to be of great significance. The results indicate that the susceptibility is at least 3 times too small to derive this system through a transition to the antiferromagnetic state, and the authors discuss possible reasons for this failure