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In this paper we describe in detail the implementation and main properties ofa new inversion code for the polarized radiative transfer equation (VFISV: VeryFast inversion of the Stokes vector). VFISV will routinely analyze pipelinedata from the Helioseismic and Magnetic Imager (HMI) on-board of the SolarDynamics Observatory (SDO). It will provide full-disk maps (4096$\times$4096pixels) of the magnetic field vector on the Solar Photosphere every 10 minutes.For this reason VFISV is optimized to achieve an inversion speed that willallow it to invert 16 million pixels every 10 minutes with a modest number(approx. 50) of CPUs. Here we focus on describing a number of importantdetails, simplifications and tweaks that have allowed us to significantly speedup the inversion process. We also give details on tests performed with datafrom the spectropolarimeter on-board of the Hinode spacecraft.

VFISV: Very Fast Inversion of the Stokes Vector for the Helioseismic and Magnetic Imager