To deepen the analysis of the photometric properties of the umbra of a sunspot, we study proper motions of small features such as umbral dots (UDs) inside a single sunspot observed by SOT of Hinode close to the disk center. We consider horizontal flows with high precision and details to study transient motion behavior of UDs in short time intervals. Blue continuum images were first deconvolved with the PSF, such that the stray light is precisely removed and the original resolution is improved. Several images were co-added to improve the S/N ratio keeping a reasonable temporal resolution and checking that the results are reproducible. The Fourier local correlation tracking (FLCT) technique is applied to the new corrected time sequence of images and horizontal velocity maps were obtained both for the whole umbra (16 ×12 ) and for a high resolution small region of the umbra (3.5 ×3.5 ) to study the smallest details of the velocity fields. We used two different Gaussian tracking windows (0.8 and 0.2 arcsec) which reveals two types of horizontal motions for umbral features. First, a global inner penumbra and peripheral umbra inward motion directed to the central parts is revealed as an overall proper motion of bright peripheral fine structures. Second, motions matching small cells inside the darkest parts of the umbra with apparent sink and source areas suggesting possible upflows and downflows appearing in different bright and dark locations without a definite answer regarding their brightness identification with a convective or a buoyant cell.