[en] The SLAC Linac is being upgraded for the use in the SLAC Linear Collider (SLC). The improved Linac must accelerate electron and positron bunches from 1.2 GeV to 50 GeV while producing output energy spectra of about 0.2%. The energy spectra must be maintained during operation to provide for good beam transmission and to minimize chromatic effects in the SLC ARCs and Final Focus. the energy spectra of these beams are determined by the bunch length and intensity, the RF phase and waveform and the intra-bunch longitudinal wakefields. A non-destructive energy spectrum monitor has been designed using a vertical wiggler magnet located downstream of the horizontal beam splitter at the end of the SLC Linac. It produces synchrotron radiation which is viewed in an off-axis x-ray position sensitive detector. The expected resolution is 0.08%. The design considerations of this monitor are presented in this paper. A pair of these monitors is under construction with an installation date set for late summer 1986. 5 refs., 6 figs