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This is the fourth paper in a series aimed at finding high-redshift quasarsfrom five-color imaging data taken along the Celestial Equator by the SDSS.during its commissioning phase. In this paper, we use the color-selected sampleof 39 luminous high-redshift quasars presented in Paper III to derive theevolution of the quasar luminosity function over the range of 3.6<z<5.0, and-27.5<M_1450<-25.5 (Omega=1, H_0=50 km s^-1 Mpc^-1). We use the selectionfunction derived in Paper III to correct for sample incompleteness. Theluminosity function is estimated using three different methods: (1) the 1/V_aestimator; (2) a maximum likelihood solution, assuming that the density ofquasars depends exponentially on redshift and as a power law in luminosity and(3) Lynden-Bell's non-parametric C^- estimator. All three methods giveconsistent results. The luminous quasar density decreases by a factor of ~ 6from z=3.5 to z=5.0, consistent with the decline seen from several previousoptical surveys at z<4.5. The luminosity function follows psi(L) ~ L^{-2.5} forz~4 at the bright end, significantly flatter than the bright end luminosityfunction psi(L) \propto L^{-3.5} found in previous studies for z<3, suggestingthat the shape of the quasar luminosity function evolves with redshift as well,and that the quasar evolution from z=2 to 5 cannot be described as pureluminosity evolution. Possible selection biases and the effect of dustextinction on the redshift evolution of the quasar density are also discussed.Comment: AJ accepted, with minor change

High-Redshift Quasars Found in Sloan Digital Sky Survey Commissioning Data. IV. Luminosity Function from the Fall Equatorial Stripe Sample