Abstract: In this note the authors construct new $p$-harmonic morphisms by studying the $p$-tension field under changes of metrics for horizontally conformal submersions. In particular, the authors explicitly construct new $\frac{10}{3}$-harmonic morphism $\phi:R^4\setminus \{0\}\rightarrow R^3$ with respect to standard Euclidean metrics. Finally the authors characterize $p$-harmonic morphisms with one dimensional fibres (globally) in terms of principal bundles.

Key words: $p$-harmonic morphism, Horizontally conformal submersion, Principal bundle