This paper presents a parallel out-of-core algorithm to invert huge dense matrices, that is matrices larger than the available physical memory by one or more orders of magnitude. Preliminary performance results are shown for a commodity cluster. An accurate prediction performance model of the algorithm is given. Thanks to the prediction model, optimizations that avoid the overhead of the out-of-core algorithm are derived. Performance of the optimized algorithm using O(N) memory size are similar to the performance of the best known parallel in-core algorithm using O(N2) memory size (where N is the matrix order). There is no memory restriction for inversion of huge matrices!