Electronic check schemes are more efficient than electronic coin scheme with respect to computational costs and the amount of information exchanged. In spite of these, difficulties in making a refund reusable and in representing the face value of a check have discouraged its development. In this paper, a new online electronic check system is presented, which solves the above problems. This system uses the partially blind signature to provide user anonymity and to represent the face value of a check. The partially blind signature enables us to make the format of refunds and initially withdrawn checks identical. Thus, it allows refunds to be reused to buy goods without any limitatiosn. Both initially withdrawn checks and refunds in our system guarantee untraceability as well as unlinkability. We also use a one-time secret key as the serial number of a check to increase the efficiency of payments. The presented check system also provides multiple offline shopping sessions to minimize the number of online messages handled by a bank. During the multiple offline shopping session, we use a one-way accumulator to provide non-repudiation service. We also analyze our new systems our new system`s security, efficiency, and atomicity.