A revisited electronic structure study of iron pyrite, FeS2, has been performed using a new Tight-Binding Linear Muffin-Tin Orbital (TB-LMTO) technique in which the radii of overlapping MT spheres are determined from a full potential construction. The interstitial spheres were chosen to provide an efficient packing of space while ensuring that the overlap between the spheres remain small. We have found that this treatment of interstitial spheres results in a dramatic improvement in the description of the electronic structure and the binding energy curves for FeS2 in comparison with a previous LMTO calculation. In particular, the energy band gap, the equilibrium lattice constant and the bulk modulus are all in much better agreement with experimental observations. Moreover, the calculated equation of state is in excellent accord with recent measured P- V data up to pressures of 15GPa with overall deviations of less than 10%. The predicted reflectivity spectrum of FeS2 as a function of pressure gives the observed behaviour of the optical edge. The bonding behaviour the orthorhombic marcasite phase of FeS2 is also discussed within this new TB-LMTO formalism.