  It was originally thought that Bonnor's solution in Einstein-Maxwell theory
describes a singular point-like magnetic dipole. Lately, however, it has been
demonstrated that indeed it may describe a black {\it dihole}, i.e., a pair of
static, oppositely-charged extremal black holes with regular horizons.
Motivated particularly by this new interpretation, in the present work, the
construction and extensive analysis of a solution in the context of the
Brans-Dicke-Maxwell theory representing a black dihole are attempted. It has
been known for some time that the solution-generating algorithm of Singh and
Rai produces stationary, axisymmetric, charged solutions in Brans-Dicke-Maxwell
theory from the known such solutions in Einstein-Maxwell theory. Thus this
algorithm of Singh and Rai's is employed in order to construct a Bonnor-type
magnetic black dihole solution in Brans-Dicke-Maxwell theory from the known
Bonnor solution in Einstein-Maxwell theory. The peculiar feature of the new
solution including internal infinity nature of the symmetry axis and its
stability issue have been discussed in full detail.
