We present a full-potential band-structure scheme based on the Linear combi
nation of overlapping nonorthogonal orbitals. The crystal potential and den
sity are represented as a lattice sum of local overlapping nonspherical con
tributions. The decomposition of the exchange and correlation potential int
o local parts is done using a technique of partitioning of unity resulting
in local shape functions, which add exactly to unity in the whole crystal a
nd which are very easily treated numerically. The method is all-electron, w
hich means that core relaxation is properly taken into account. Nevertheles
s, the eigenvalue problem is reduced to the dimension of a minimum valence
orbital basis only. Calculations on sp and transition metals give results c
omparable to other full-potential methods. The calculations on the diamond
lattice demonstrate the applicability of our approach to open structures. T
he consequent local description of all real-space functions allows the trea
tment of substitutional disordered materials. [S0163-1829(99)09303-0].