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Extended X-ray absorption fine structure (EXAFS) conducted on an equiatomic MoNbTaW bcc medium-entropy alloy that was annealed at 2273 K reveals unexpectedly small 1st and 2nd shell element-specific lattice distortions. An experimental size-mismatch parameter, δexp, is determined to be ca. 50% lower than the corresponding calculated value. Around W, short-range order (SRO) preferring 4d elements in the 1st and 2nd shells persists. A Nb-W ordering is found, which is reminiscent of ordering emerging at lower temperatures in the B2(Mo,W;Ta,Nb)- and B32(Nb,W)-phases. With high-temperature ordering preferences in fcc also foreshadowing low-temperature phase, these findings suggest a general feature of high-temperature SRO.