We examined the morphologies of two-phase emulsions in the ternary 2-butoxyethanol/n-decane/water system at various temperatures and water-to-oil ratios (WORs). The two-phase emulsion morphologies depended on temperature, WOR, and amphiphile concentration, and the results are presented in a temperature-amphiphile concentration coordinate system or a "fish" diagram. The observations made in this work contradict the predictions by the phase-inversion-temperature (PIT) concept. At WOR<1, a vertical inversion line was observed at T<T(lc) (lower critical endpoint temperature), dividing the two-phase region into the subregions of B/T (W/O) and T/B (O/W) emulsions. At T>T(uc) (upper critical endpoint temperature) and at low amphiphile concentrations, only B/T emulsions appeared, irrespective of temperature. At WOR>1, the situation was reversed; T/B emulsions at T<T(lc), T/B and B/T emulsions at T>T(uc), and T/B emulsions at low amphiphile concentrations, irrespective of temperature. At WOR=1, two horizontal inversion lines, one each at T<T(lc) and T>T(uc), were observed. The morphologies of the two-phase emulsions were B/T or T/B emulsions at low amphiphile concentrations, and at higher amphiphile concentrations T/B at T<T(lc) and B/T at T>T(uc). All these findings along with three-phase emulsion data result in complete emulsion morphology diagrams in the temperature-amphiphile concentration space or fish diagram.