The Transformer, with its scaled dot-product attention mechanism, has become a foundational architecture in modern AI. However, this mechanism is computationally intensive and incurs substantial energy costs. We propose a new Transformer architecture EcoTransformer, in which the output context vector is constructed as the convolution of the values using a Laplacian kernel, where the distances are measured by the L1 metric between the queries and keys. Compared to dot-product based attention, the new attention score calculation is free of matrix multiplication. It performs on par with, or even surpasses, scaled dot-product attention in NLP, bioinformatics, and vision tasks, while consuming significantly less energy. (This version (v2) supersedes v1 and reflects the intended release and licensing.)