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In this paper, we propose a novel noniterative algorithm to simultaneously estimate optimal rigid transformations for serial section images, which is a key component in performing volume reconstructions of serial sections of biological tissue. To avoid the error accumulation and propagation caused by current algorithms, we add an extra condition: that the positions of the first and last section images should remain unchanged. This constrained simultaneous registration problem has not previously been solved. Our solution is noniterative; thus, it can simultaneously compute rigid transformations for a large number of serial section images in a short time. We demonstrate that our algorithm obtains optimal solutions under ideal conditions and shows great robustness under nonideal circumstances. Further, we experimentally show that our algorithm outperforms state-of-the-art methods in terms of speed and accuracy.