Although pre-trained language models (PLMs) are effective for natural language understanding (NLU) tasks, they demand a huge computational resource, thus preventing us from deploying them on edge devices. Researchers have therefore applied compression techniques for neural networks, such as pruning, quantization, and knowledge distillation, to the PLMs. Although these generic techniques can reduce the number of internal parameters of hidden layers in the PLMs, the embedding layers tied to the tokenizer arehard to compress, occupying a non-negligible portion of the compressed model. In this study, aiming to further compress PLMs reduced by the generic techniques, we exploit frequency-aware sparse coding to compress the embedding layers of the PLMs fine-tuned to downstream tasks. To minimize the impact of the compression on the accuracy, we retain the embeddings of common tokens as they are and use them to reconstruct embeddings of rare tokens by locally linear mapping. Experimental results on the GLUE and JGLUE benchmarks for language understanding in English and Japanese confirmed that our method can further compress the fine-tuned DistilBERT models models while maintaining accuracy.