Minimal space with non-minimal square

We completely solve the problem whether the product of two compact metric spaces admitting minimal maps also admits a minimal map. Recently Boroński, Clark and Oprocha gave a negative answer in the particular case when homeomorphisms rather than continuous maps are considered. In the present paper we show that there is a metric continuum \(X\) admitting a minimal map, in fact a minimal homeomorphism, such that \(X\times X\) does not admit any minimal map.