Efficient inference of Multi-Head Latent Attention (MLA) is challenged by deploying the DeepSeek-R1 671B model on a single Multi-GPU server. This paper introduces FlashMLA-ETAP, a novel framework that enhances MLA inference for the single-instance deployment scenario on NVIDIA H20 GPUs. We propose the Efficient Transpose Attention Pipeline (ETAP), which reconfigures attention computation through transposition to align the KV context length with the \(M\)-dimension in WGMMA operations, significantly reducing redundant computations. FlashMLA-ETAP achieves a 2.78x speedup over FlashMLA at 64K sequence length (batch size 16), with 5.24x and 4.94x improvements over FlashAttention-3 and FlashInfer, respectively, while maintaining numerical stability with a 15.2x lower RMSE (\(1.25 \times 10^{-5}\)) than FlashAttention-3. Furthermore, ETAP's design enables seamless integration into frameworks like FlashAttention-3 and FlashInfer, supported by a detailed theoretical analysis. Our work addresses a critical gap in resource-constrained inference, offering a scalable solution for mid-tier GPUs and paving the way for broader adoption in hardware-aware optimization. Code is available at https://github.com/pengcuo/FlashMLA-ETAP.