A digraph (that is a directed graph) is said to be highly arc transitive if its automorphism group is transitive on the set of s-arcs for each s greater-than-or-equal-to 0. Several new constructions are given of infinite highly are transitive digraphs. In particular, for DELTA a connected, 1-arc transitive, bipartite digraph, a highly arc transitive digraph DL(DELTA) is constructed and is shown to be a covering digraph for every digraph in a certain class D(DELTA) of connected digraphs. Moreover, if DELTA is locally finite, then DL(DELTA) is a universal covering digraph for D(DELTA). Further constructions of infinite highly arc transitive digraphs are given.