Non-binary M-ary words processed by data entry systems often suffer from asymmetric errors. In character recognition systems, for example, two symbols a_i and a_j with similar shapes have a high probability of being mistaken for one another. Among the many types of data processed by data entry systems, M-ary words selected from a specified codebook, such as postal codes and product numbers, should be strongly protected from asymmetric errors because these words are often used for indexing a database. This paper proposes a new class of nonsystematic M-ary asymmetric error correcting codes which can be utilized to generate these codebooks. In order to effectively correct asymmetric errors, the new class of codes is designed based on a multilevel coding method and a set partitioning algorithm. Evaluation shows that the proposed codes have a low decoded symbol error rate.