  We give a full description of the $BV$-structure on the Hochschild cohomology
of exceptional local algebras of quaternion type, defined by parameters
$(k,0,d)$ in case of even parameter $k \geqslant 3$, according to Erdmann's
classification. We develop and use the method of comparison morphisms and weak
self-homotopy method. This article states as a generalization of similar
results about $BV$-structures on Hochscild cohomology of algebras of quaternion
type.
