We present the results of the first detection of submillimeter water maser emission toward water-fountain nebulae. Using APEX we found emission at 321.226 GHz toward two sources: IRAS 18043−2116, and IRAS 18286−0959. The submillimeter H2O masers exhibit expansion velocities larger than those of the OH masers, suggesting that these masers, similarly to the 22 GHz masers, originate in fast bipolar outflows. The 321 GHz masers in IRAS 18043−2116 and IRAS 18286−0959, which figure among the sources with the fastest H2O masers, span a velocity range similar to that of the 22 GHz masers, indicating that they probably coexist. The intensity of the submillimeter masers is comparable to the 22 GHz masers, implying that the kinetic temperature of the region where the masers originate is Tk>1000 K. We propose a simple model invoking the passage of two shocks through the same gas that creates the conditions for explaining the strong high-velocity 321 GHz masers coexisting with the 22 GHz masers in the same region.