My aim is to sketch a proof of the second assertion by J. Deny at the end of my paper [1] of 1945, and also to obtain all of the harmonic homeomorphisms of an open disk onto iteself. LetDD′ be two copies of the open unit disk, and letDD′ be their boundariesx2+y2= 1. LetHdenote the set of harmonic homeomorphisms (or harmonic mappings) ofDontoD′ and letMbe the use set of harmonic extensions toDof continuous suriectionsg= (g1g2) ofContoC′ which aremonotonein the sense that for eact θ′ ∈C′g-1(θ′) is connected (and is therefore a closed are ofC). thenH=M.