  Halmos' two projections theorem for Hilbert space operators is one of the
fundamental results in operator theory. In this paper, we introduce the term of
two harmonious projections in the context of adjointable operators on Hilbert
$C^*$-modules, extend Halmos' two projections theorem to the case of two
harmonious projections. We also give some new characterizations of the closed
submodules and their associated projections. As an application, a norm equation
associated to a characterization of the Friedrichs angle is proved to be true
in the framework of Hilbert $C^*$-modules.
