  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.
