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The ability to generate small transverse emittance is perhaps the main limiting factor for the performance of high-gain x-ray free-electron lasers (FELs). Noting that beams from an rf photocathode gun can have energy spread much smaller than required for efficient FEL interaction, we present a method to produce normalized transverse emittance at or below about 0.1   μm, which will lead to a significantly shorter length undulator as well as a lower electron beam energy for an x-ray FEL project. The beam manipulation consists of producing an unequal partition of the initially equal emittances into two dissimilar emittances by a flat-beam technique and exchanging the larger transverse emittance with a smaller longitudinal emittance. We study various issues involved in the manipulation. In particular, a new emittance exchange optics we found enables an exact emittance exchange necessary for this scheme.