Due to the emergence of data-driven technologies in Aotearoa New Zealand that use Māori data, there is a need for values-based frameworks to guide thinking around balancing the tension between the opportunities these create, and the inherent risks that these technologies can impose. Algorithms can be framed as a particular use of data, therefore data frameworks that currently exist can be extended to include algorithms. Māori data sovereignty principles are well-known and are used by researchers and government agencies to guide the culturally appropriate use of Māori data. Extending these principles to fit the context of algorithms, and re-working the underlying sub-principles to address issues related to responsible algorithms from a Māori perspective leads to the Māori algorithmic sovereignty principles. We define this idea, present the updated principles and subprinciples, and highlight how these can be used to decolonise algorithms currently in use, and argue that these ideas could potentially be used to developed Indigenised algorithms.