This paper introduces a new method of bookkeeping called Triple Entry Accounting (TEA), which combines financial cryptography innovations like the signed receipt with traditional double entry bookkeeping. The signed receipt, a digital record with strong reliability and security, is signed by all three parties involved in a transaction (Alice, Bob, and Ivan) and serves as a fact-based record, reducing the need for double entry. This approach challenges the traditional double entry system by expanding its application from within firms to between firms, making it more robust and transparent. The paper discusses the historical development of accounting methods, from single entry to double entry, and highlights the limitations of single entry in handling errors and fraud. It then delves into the concept of the signed receipt, explaining how it can be used to create reliable and trustworthy entries in accounting systems. The signed receipt is presented as a core component of TEA, which can be implemented in various ways, including using blockchain technology. The paper also explores the patterns of commerce that can be supported by TEA, such as shared transaction repositories and the integration of digital cash into corporate accounting systems. It outlines the requirements for implementing TEA, including strong pseudonymity, integrated application-level messaging, and defining the set of transactions. Finally, the paper concludes by discussing the benefits of TEA in enhancing governance and fraud detection, and its potential to revolutionize corporate and public accounting.This paper introduces a new method of bookkeeping called Triple Entry Accounting (TEA), which combines financial cryptography innovations like the signed receipt with traditional double entry bookkeeping. The signed receipt, a digital record with strong reliability and security, is signed by all three parties involved in a transaction (Alice, Bob, and Ivan) and serves as a fact-based record, reducing the need for double entry. This approach challenges the traditional double entry system by expanding its application from within firms to between firms, making it more robust and transparent. The paper discusses the historical development of accounting methods, from single entry to double entry, and highlights the limitations of single entry in handling errors and fraud. It then delves into the concept of the signed receipt, explaining how it can be used to create reliable and trustworthy entries in accounting systems. The signed receipt is presented as a core component of TEA, which can be implemented in various ways, including using blockchain technology. The paper also explores the patterns of commerce that can be supported by TEA, such as shared transaction repositories and the integration of digital cash into corporate accounting systems. It outlines the requirements for implementing TEA, including strong pseudonymity, integrated application-level messaging, and defining the set of transactions. Finally, the paper concludes by discussing the benefits of TEA in enhancing governance and fraud detection, and its potential to revolutionize corporate and public accounting.