We explore the structural evolution of Tc-n (n = 4-20) clusters using a first-principles global minimization technique, namely, basin-hopping from density functional theory geometry optimization (BH-DFT). Significantly more stable structures have been found in comparison with previous models, indicating the power of DFT-based basin hopping in finding new structures for clusters. The growth sequence and pattern for n from 4 to 20 are analyzed from the perspective of geometric shell formation. The binding energy per atom, relative stability, and magnetic moments are examined as a function of the cluster size. Several magic sizes of higher stability and symmetry are discovered. In particular, we find that Tc-19 prefers an O-h symmetry structure, resembling a piece of a face-centered-cubic metal, and its electrostatic potential map shows interesting features that indicate special reactivity of the corner atoms.