The purpose of this study is to show a class of near shift-invariant and orientation-selective transform based on even-stacked cosine-modulated filter banks (ECFBs) which originally have been proposed by Lin and Vaidyanathan. It is well-known that ECFBs can be designed by the modulation of just one prototype filter and guarantee the linear phase property. We extend this class to delay-less oversampled ECFB and show two additional attractive features; high directional selectivity and near shift-invariant property. In this paper, these properties are verified by theoretical analysis and demonstrations.