In this paper, we propose a novel Single Noisy Audio De-noising Framework (SNA-DF) for speech denoising using only single noisy audio samples, which overcomes the limi-tation of constructing either noisy-clean training pairs or multiple independent noisy audio samples. The proposed SNA-DF contains two modules: training audio pairs gener-ated module and audio denoising module. The first module adopts a random audio sub-sampler on single noisy audio samples for the generation of training audio pairs. The sub-sampled training audio pairs are then fed into the audio denoising module, which employs a deep complex U-Net incorporating a complex two-stage transformer (cTSTM) to extract both magnitude and phase information for taking full advantage of the complex features of single noisy au-dios. Experimental results show that the proposed SNA-DF not only eliminates the high dependence on clean targets of traditional audio denoising methods, but also outperforms the methods using multiple noisy audio samples.