A terahertz (THz) electromagnetically-induced transparency (EIT) phenomenon is observed from two types of self-complementary meta-molecules (MMs) based on rectangular shaped electric split-ring resonators (eSRR) on Croatian checkerboard. Each MM contains a couple of identical size eSRRs and a couple of structural inversed eSRRs twisted π/2 in checkerboard pattern. In the first type of MM (type-I), the gap is in the middle line of eSRR. In the second type of MM (type-II), the gap is on the two arms of eSRR. Both types of MMs exhibit EIT effect. A maximum 20 ps group delay is observed at the transparency window of 0.63 THz in type-I MM; while a maximum 6.0 ps group delay is observed at the transparent window of 0.60 THz in type-II MM. The distribution of surface currents and electrical energy reveals that only CeSRR contribute to the transparency window as well as the side-modes in type-I MM, where the current leakage via contact point contributes to the low-frequency side-mode, and the coupled local inductive-capacitive (LC) oscillation in CeSRRs contributes to the high-frequency side-mode. In type-II MM, however, the localized dipolar oscillator of CeSRR contributes to the low-frequency side-mode; while the hybridization of dipole oscillation on eSRR and LC resonance on CeSRR contributes to the high-frequency side-modes. Our experimental findings manifest a new approach to develop THz slow-light devices.