This paper presents a method of temporal decomposition (TD) for line spectral frequency (LSF) parameters, called "Modified Restricted Temporal Decomposition" (MRTD), and its application to low rate speech coding. The LSF parameters have not been used for TD due to the stability problems in the linear predictive coding (LPC) model. To overcome this deficiency, a refinement process is applied to the event vectors in the proposed TD method to preserve their LSF ordering property. Meanwhile, the restricted second order TD model, where only two adjacent event functions can overlap and all event functions at any time sum up to one, is utilized to reduce the computational cost of TD. In addition, based on the geometric interpretation of TD the MRTD method enforces a new property on the event functions, named the "well-shapedness" property, to model the temporal structure of speech more effectively. This paper also proposes a method for speech coding at rates around 1.2 kbps based on STRAIGHT, a high quality speech analysis-synthesis method, using MRTD. In this speech coding method, MRTD based vector quantization is used for encoding spectral information of speech. Subjective test results indicate that the speech quality of the proposed speech coding method is close to that of the 4.8 kbps FS-1016 CELP coder.