We study linkage of \((d+1)\) -fold quadratic Pfister forms over function fields in one variable over a henselian valued field of 2-cohomological dimension d. Specifically, we characterise this property in terms of linkage of quadratic Pfister forms over function fields over the residue field of the henselian valued field; in full generality in characteristic different from 2, and for most complete discretely valued fields in characteristic 2. As an application, we obtain a proof that \((d+2)\) -fold quadratic Pfister forms over function fields in one variable over a d-dimensional higher local field are linked.
