Using an improved calculation method, the transmission coefficient of a quadruple barrier resonant tunneling diode is calculated. Using this result, extreme values of the transmission coefficient and the full widths at half maximum (FWHM) of the resonant peaks are calculated. It is shown that the first terms of the expressions |θ|, which are proportional to the FWHM, are given by the same formula in double, triple, and quadruple barrier diodes.