A new algorithm to compute spin lattice relaxation (T1) maps in magnetic resonance imaging (MRI) by using fast imaging protocols and monitoring the magnetization evolution towards a steady state is proposed. This algorithm uses a general least squares fit to multiple point experimental data and is thus much more precise than the standard two point fit. Since this imaging protocol is designed to consume time comparable to that of standard clinical protocols, it has an advantage in comparison to traditional multiple point protocols, which require considerably longer scanning times. In addition to T1 maps the protocol can generate final images suitable for clinical diagnosis. Thus it is possible to generate relaxation data without considerably lengthening the total required MRI study time. The results of phantom testing of this protocol are reported. © 1986, American Institute of Physics for the National Institute of Standards and Technology. All rights reserved.