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The problem of basket recommendation~(BR) is to recommend a ranking list of items to the current basket. Existing methods solve this problem by assuming the items within the same basket are correlated by one semantic relation, thus optimizing the item embeddings. However, this assumption breaks when there exist multiple intents within a basket. For example, assuming a basket contains \{\textit{bread, cereal, yogurt, soap, detergent}\} where \{\textit{bread, cereal, yogurt}\} are correlated through the "breakfast" intent, while \{\textit{soap, detergent}\} are of "cleaning" intent, ignoring multiple relations among the items spoils the ability of the model to learn the embeddings. To resolve this issue, it is required to discover the intents within the basket. However, retrieving a multi-intent pattern is rather challenging, as intents are latent within the basket. Additionally, intents within the basket may also be correlated. Moreover, discovering a multi-intent pattern requires modeling high-order interactions, as the intents across different baskets are also correlated. To this end, we propose a new framework named as \textbf{M}ulti-\textbf{I}ntent \textbf{T}ranslation \textbf{G}raph \textbf{N}eural \textbf{N}etwork~({\textbf{MITGNN}}). MITGNN models $T$ intents as tail entities translated from one corresponding basket embedding via $T$ relation vectors. The relation vectors are learned through multi-head aggregators to handle user and item information. Additionally, MITGNN propagates multiple intents across our defined basket graph to learn the embeddings of users and items by aggregating neighbors. Extensive experiments on two real-world datasets prove the effectiveness of our proposed model on both transductive and inductive BR. The code is available online at https://github.com/JimLiu96/MITGNN.