a closed linear relation and the multivalued part $\mul T$ is invariant under $B$, then the product is a maximal sectorial relation; cf. [@HSSW17]. However, in fact, the relation $$\label{tbt}
T^{*}(I+iB)T$$ is maximal sectorial for any closed linear relation $T$. This will be shown in this note via a matrix decomposition of $B$ with respect to the orthogonal decomposition $\sH=\cdom T^* \oplus \mul T$. In addition the closed sectorial form corresponding to $T^{*}(I+iB)T$ will be determined. The main argument consists of a reduction to the case where $T$ is an operator. For the convenience of the reader the arguments in the operator case are included. Note that if $T$ is not closed, then $T^{*}(I+iB)T$ is a sectorial relation which may have maximal sectorial extensions, such as $T^{*}(I+iB)T^{**}$ and some of these extensions have been determined in [@HSS19]; cf. [@ST12].

It is clear that the sum of two sectorial relations is a sectorial relation and there will be maximal sectorial extensions. In [@HSS19] the Friedrichs extension has been determined in general, while the Kreĭn extension has been determined only under additional conditions. As an application of the above results for the relation in the Kreĭn extension and, in fact, all extremal 