Digital filtering techniques are indispensable tools for analyzing and evaluating surface topography data. Among the conventional digital filters, the Gaussian filter is the most commonly used filtering technique for both one-dimensional and two-dimensional data. This is because of isotropic and zero-phase transmission characteristics. However, in the filtering process with the Gaussian filter, additional run-in and run-out regions are usually needed due to its large end-effects. To overcome this disadvantage that supplementary profile data are needed to reduce the end-effects, the one-dimensional spline filter was introduced. At present, it is widely accepted as a practical filtering technique and published as ISO/TC16610-22. In fact, a successive application of the one-dimensional spline filter to the two-dimensional data in the orthogonal directions may lead to an anisotropic amplitude characteristic. In this paper, a purely two-dimensional discrete spline filter is proposed and its computational procedure is also described, which is able to approximate the isotropic frequency response in an ideal manner through a least-squares optimization technique.