Spin-echo measurements on lssW were performed with dilute alloys of W (0.1, 0.25, 0.5 and 1 at %) in Fe. The result for the hyperfine field: This is the first case of a very large hyperfine anomaly in electronic hyperfine fields which is not caused by the pathological cancellation of orbital and spin magnetism in jackknife Pl/2 or d3/z single proton configurations.A detailed discussion shows that the large hyperfine anomaly may be related to the anomalously small magnetic dipole moment of ~S3W. Our result should stimulate further theoretical work with the aim to understand this magnetic moment as well as the giant hyperfine anomaly.