  The classical Vaidya metric is transformed to the special diagonal
coordinates in the case of the linear mass function allowing rather easy
treatment. We find the exact analytical expressions for metric functions in
these diagonal coordinates. Using these coordinates, we elaborate the maximum
analytic extension of the Vaidya metric with a linear growth of the black hole
mass and construct the corresponding Carter-Penrose diagrams for different
specific cases. The derived global geometry seemingly is valid also for a more
general behavior of the black hole mass in the Vaidya metric.
