  In 1978, Richard Rado showed that every edge-coloured complete graph of
countably infinite order can be partitioned into monochromatic paths of
different colours. He asked whether this remains true for uncountable complete
graphs and a notion of \emph{generalised paths}. In 2016, Daniel Soukup
answered this in the affirmative and conjectured that a similar result should
hold for complete bipartite graphs with bipartition classes of the same
infinite cardinality, namely that every such graph edge-coloured with $r$
colours can be partitioned into $2r-1$ monochromatic generalised paths with
each colour being used at most twice.
  In the present paper, we give an affirmative answer to Soukup's conjecture.
