Motivated by the desire to image exosolar planets, recent work by us and others has shown that high-contrast imaging can be achieved using specially shaped pupil masks. To date, the masks we have designed have been symmetric with respect to a cartesian coordinate system but were not rotationally invariant, thus requiring that one take multiple images at different angles of rotation about the central point in order to obtain high-contrast in all directions. In this paper, we present a new class of masks that have rotational symmetry and provide high-contrast in all directions with just one image. These masks provide the required 10^{-10} level of contrast to within 4 lambda/D, and in some cases 3 lambda/D, of the central point, which is deemed necessary for exosolar planet finding/imaging. They are also well-suited for use on ground-based telescopes, and perhaps NGST too, since they can accommodate central obstructions and associated support spiders.

20 pages, 9 figures, to appear in ApJ