  The phase diagram of $\alpha$-cyclodextrin/water/4-methylpyridine solutions,
a system undergoing inverse melting, has been studied by differential scanning
calorimetry, rheological methods, and X-rays diffraction. Two different fluid
phases separated by a solid region have been observed in the high
$\alpha$-cyclodextrin concentration range ($c$$\geq$150 mg/ml). Decreasing $c$,
the temperature interval where the solid phase exists decreases and eventually
disappears, and a first order phase transition is observed between the two
different fluid phases.
