Deep neural networks (DNNs) have made breakthroughs in various fields including image recognition and language processing. DNNs execute hundreds of millions of multiply-and-accumulate (MAC) operations. To efficiently accelerate such computations, analog in-memory-computing platforms have emerged leveraging emerging devices such as resistive RAM (RRAM). However, such accelerators face the hurdle of being required to have sufficient on-chip crossbars to hold all the weights of a DNN. Otherwise, RRAM cells in the crossbars need to be reprogramed to process further layers, which causes huge time/energy overhead due to the extremely slow writing and verification of the RRAM cells. As a result, it is still not possible to deploy such accelerators to process large-scale DNNs in industry. To address this problem, we propose the BasisN framework to accelerate DNNs on any number of available crossbars without reprogramming. BasisN introduces a novel representation of the kernels in DNN layers as combinations of global basis vectors shared between all layers with quantized coefficients. These basis vectors are written to crossbars only once and used for the computations of all layers with marginal hardware modification. BasisN also provides a novel training approach to enhance computation parallelization with the global basis vectors and optimize the coefficients to construct the kernels. Experimental results demonstrate that cycles per inference and energy-delay product were reduced to below 1% compared with applying reprogramming on crossbars in processing large-scale DNNs such as DenseNet and ResNet on ImageNet and CIFAR100 datasets, while the training and hardware costs are negligible.