Large current in a chip can cause problems such as noise and power consumption. In this paper, a vectorless approach to analyzing a tight upper bound on the maximum instantaneous current (MIC) of a circuit is proposed. Several types of signal correlations that can cause the MIC estimation to lose accuracy are first described. Next, taking signal correlations into account, theorems to identify gates that switch mutually exclusively are proposed. In particular, the proposed algorithm can naturally consider signal correlations across sequential elements (flip-flops), whereas previous research on this topic addressed combinational circuits only. After deriving the information of mutually exclusive switching, a graph algorithm is applied to obtain an upper bound on the MIC. On average, the obtained sequential benchmark results are 179% tighter than those from the iMax algorithm and 66% tighter than those from the partial input enumeration algorithm