A new model is developed for the collisional Weibel instability based upon a Cartesian tensor expansion of the electron Fokker-Planck equation. Its results are substantially different from those predicted by an equivalent 2 electron fluid model (Mochizuki et al. 1980). Growth rates ( approximately 1011 s-1) and optimum wavelengths ( approximately 10 mu m) correlate well with experimental observations of filamentary structures in laser-plasmas. The model suggests that the instability may disrupt implosion symmetry, particularly for high-Z targets irradiated by short wavelength lasers.