In this paper, we extend the conventional error-trellis construction for convolutional codes to the case where a given check matrix H(D) has a factor Dl in some column (row). In the first case, there is a possibility that the size of the state space can be reduced using shifted error-subsequences, whereas in the second case, the size of the state space can be reduced using shifted syndrome-subsequences. The construction presented in this paper is based on the adjoint-obvious realization of the corresponding syndrome former HT(D). In the case where all the columns and rows of H(D) are delay free, the proposed construction is reduced to the conventional one of Schalkwijk et al. We also show that the proposed construction can equally realize the state-space reduction shown by Ariel et al. Moreover, we clarify the difference between their construction and that of ours using examples.