  A new method is applied for deriving the redshift and shadow of a
Schwarzschild black hole moving freely in the de Sitter expanding universe as
recorded by a co-moving remote observer. This method is manly algebraic
focusing on the transformation of the conserved quantities under the de Sitter
isometry relating the black hole proper co-moving frame to observer's one.
Hereby one extracts the general expressions of the redshifts and shadows of the
black holes having peculiar velocities but their expressions are too extended
to be written down here. Therefore, only some particular cases and intuitive
expansions are presented while the complete results are given in an algebraic
code on computer \cite{Comp}.
