An algorithm for computing the LSP frequencies will be given in this paper. The algorithm employs a recursive technique to generate the line spectrum from the reflection coefficients. In each step of a recursion, a scaling and rotation on the complex frequency plane are required. The even and odd line spectral frequencies are found to be the zero cross-points on the real and imaginary axis respectively. The algorithm does not require to calculate the LPC coefficients and it can be implemented using fixed-point arithmetic with low complexity.