It is shown how it is possible to simultaneously record images of all four Stokes parameters with a single CCD detector chip when fast (50 kHz), piezoelastic modulation of the polarization state is used. As the four image planes use the identical pixels of the CCD, all gain-table or flat-field effects vanish when forming the fractional polarization images. For each group of four pixel rows, one row collects the photons, while the other three are used for fast buffer storage. There are no light losses caused by masking of the pixel rows used for buffer storage, sinced a microlens array collects all the photons and directs them to the unmasked pixel rows. The efficiency of the system for simultaneous recording of all four Stokes parameters is six times greater than that of ZIMPOL I, the first generation of the Zürich Imaging Stokes Polarimeter, since no beam splitter with three separate CCD cameras is needed and no significant light losses occur at the masked pixel rows. The theoretically possible efficiency limit is thereby practically reached. The system is planned to be developed as ZIMPOL II, the second generation of the Zürich Imaging Stokes Polarimeter.