Logs used in conformance checking with process models are often the event logs. Conformity between the model and the log is often measured by counting the traces which could be reconstructed and the tasks which would be evoked but were not in the running trace through rerunning the model according to the task traces in the log. However the method is not sufficiently comprehensive. While checking the model consisting of many selections with its Event Log, the conformity will be very low due to the large number of evoked tasks that are not in the running task trace. Moreover, while checking the model mainly composed by parallel branches with the log only containing sequential task traces and sharing the same task set with the model, the conformity will be very high due to the fact that only a few tasks can't be executed normally while monitoring the real behavior. To overcome the weakness of the original method, a bidirectional checking method made up of checking the accuracy of the model and checking the completeness of the log, and a new kind of log named Token Log which can describe the property of its corresponding model, are proposed in this paper. With the Token Log, the new method for conformance checking is clearer, more concise and more accurate.