An analytical presentation and numerical analysis of low-frequency (1/f) noise of a spatially inhomogeneous Schottky barrier contact (SBC) (with local barrier height lowering (BHL)) are given. The spectral intensity of the current fluctuation (SI) S-i is analysed as a function of temperature, current and contact area for various parameters of contact inhomogeneity, such as the area ratio of low barrier height region and main part of the SEC, the BHL value, the ideality factor of the BHL region and others. It is shown that local BHL can cause an essential increase of SI with lower temperature. It manifests itself as well in a deviation of current dependence of SI from the usual square law S-i - I-2, and of area dependence - from the conventional S-i - l/A for a homogeneous SEC. All the above peculiarities of noise characteristics have been observed in real silicon and gallium arsenide SBCs and can be explained on the basis of the local BHL model. A Gaussian barrier height distribution, used in a number of publications, doesn't explain the above peculiarities of real SBCs.