[en] The magnetic susceptibility and specific heat measurements were performed on YBaCo_4-xZn_xO₇ in a wide temperature range. This compound is characterized by a mixed valence of Co (Co²⁺/Co³⁺) and has a kagome-like layered magnetic arrangement of spin moments in the P6₃mc hexagonal crystal structure. This arrangement is known for strong frustration of magnetic interactions and prevents the formation of long range magnetically ordered ground states. However, peak-like anomalies were found in the magnetic susceptibility at the temperatures 66, 27, 15 and 3 K for x=0, 1, 2, 3, respectively. Small anomalies in the specific heat at the related temperatures were found for x=1, 2, 3, indicating the magnetic freezing of the spin system. Zn-substitution changes the ratio Co²⁺/Co³⁺ which strongly influences the magnitudes and temperatures of anomalies in magnetic susceptibility and specific heat. The increase of Zn content in YBaCo_4-xZn_xO₇ leads to a rapid decrease of the magnetic contribution in the specific heat in a wide temperature range