Abstract: A method for fixing pieces by freezing which consists in fixing the pieces o be machined on an auxiliary support having good thermal conductivity, for example made of aluminium, by freezing onto an freeze vice on the copper plate of which there has previously been deposited a film of antifreeze liquid. The auxiliary support is fixed to the freeze vice by vacuum, by magnetism, or by any mechanical clamping. This method makes it possible to eliminate the operation and the time for thawing which, up until now, was required for removing the pieces to be machined from the freeze vice. The auxiliary support may be used as a transfer pallet on which the pieces are held by freezing.