Extended (R similar to 4.5 kpc) X-ray emission in the Seyfert 2 galaxy NGC 4388 has been discovered with the ROSAT HRI. No evidence for a nuclear, unresolved component has been found; the upper limit for such a component is about 20% of the total flux. The interpretation of the extended emission in terms of nuclear radiation scattered by a plasma ionized by the nuclear photons can be excluded on the basis of a simple photoionization calculation. The two most likely alternatives, i.e. thermal emission from a collisionally heated plasma and the sum from many unresolved discrete sources, are briefly discussed
