The mechanism of financial transactions provided to society today cannot be determined by a single financial institution, but is determined through a complex structure of mutual cooperation, or a "network", between several financial institutions. Quantitative analysis of such a "network" structure had not been explored until recently, mainly due to limitations in the data available. This paper analyzes the "network" structure of financial transactions, using the logged data of financial transactions through the BOJ-Net (Current Account of the Bank of Japan), which became obtainable after the introduction of RTGS (Real Time Gross Settlement) in 2001. This study uses recently developed methods of statistical physics. This field of study provides an analytical framework that treats the complex structure of financial institutions as a structure of elements, or "nodes," that are connected to one another, through "links." Our study shows that the "network" of financial transactions between financial institutions possess fractal structure, similar to that observed in network structures in the natural world (such as river basins) or the structure of the Internet. We also find that financial institutions situated in the middle of the network structure hold more links than those institutions on the periphery of the network, implying that the formed structure is a result of the pursuance of "efficiency" rather than "stability." We should pay enough attention to the dynamic nature of the network structure in order to evaluate its stability, since the network structure of financial transactions is not static in nature(the network is not based upon hardware like cables, as in the case of the Internet). Thus, there is a need to confirm the stability of the network structure over time. In this respect, further analysis of "dynamic networks" is worth a try, based on the evidence shown in this paper which confirms a certain degree of robustness within the network.