[en] In the approximation of strong bond using the method of statistics of levels one studied the electron spectrum and wave functions of a new quasicrystalline structure - Fibonacci two-dimensional lattice. That was a self-similar structure consisting of three elementary structure units. Both central and apical decorations of the given structure were studied. The energy electron spectrum of the Fibonacci two-dimensional lattice was shown to contain singular part, but in contrast to the Fibonacci unidimensional lattice, the spectrum did not contain hierarchic slit structure. The measure of the permitted states (the Lebesgue measure) of the spectrum was not a zero one while in case of the central decoration it was close to 1. The mechanism of localization of wave functions was studied and their criticality was revealed