DC magnetization process of a high-quality single crystal of CeCoIn5 has been measured at low temperatures down to 50 mK. A sharp magnetization jump with a small hysteresis is observed at the upper critical field Hc2 for both a and c directions, indicating the transition to the normal state to be of first-order. Although the results might suggest a strong Pauli paramagnetic effect, no Fulde--Ferrell--Larkin--Ovchinnikov (FFLO) phase is observed.
PACS numbers: 74.25.Dw, 74.25.Ha, 74.70.Tx
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