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Most existing structured pruning methods for Large Language Models (LLMs) require substantial computational and data resources for retraining to reestablish the corrupted correlations, making them prohibitively expensive. To address this, we propose an efficient pruning framework for LLMs called Orthogonal Neuron Decomposition and Linear Calibration (Olica), which eliminates the need for retraining. A key observation is that the multi-head attention (MHA) layer depends on two types of matrix products (i.e., ${\rm W}_q{\rm W}^{\top}_k$ and ${\rm W}_v{\rm W}^{\top}_o$). By treating these matrix products as unified entities and applying principal component analysis (PCA), we extract the most important information to compress LLMs without sacrificing accuracy or disrupting their original structure. Consequently, retraining becomes unnecessary. Moreover, a fast decomposition method is devised, reducing the complexity of PCA by a factor of the square of the number of attention heads. Additionally, to mitigate error accumulation problem caused by pruning the feed-forward network (FFN) layer, we introduce a linear calibration method to reconstruct the residual errors of a pruned layer using two low-rank matrices. By leveraging singular value decomposition (SVD) on the solution of the least-squares problem, these matrices are obtained without requiring retraining. Extensive experiments show that the proposed Olica is efficient in terms of data usage, GPU memory, and running time, while delivering superior performance across multiple benchmarks.