From dielectric spectroscopy measurements on polyisoprene performed at ambient and elevated pressures, we show that the secondary relaxation has properties of the supposedly universal Johari-Goldstein beta-relaxation. These properties include approximate (i.e., in order of magnitude only) invariance of the ratio of its relaxation time tau(beta)(T,P) to the structural alpha-relaxation time tau(alpha)(T,P) to temperature T and pressure P variations provided tau(alpha)(T,P) is kept constant. Under the same condition, the frequency dispersion of the alpha-relaxation or the fractional exponent beta(KWW)(T,P) of the Kohlrausch-Williams-Watts correlation function is also unchanged. Thus, tau(alpha)(T,P) and beta(KWW)(T,P) characterizing the alpha-relaxation dynamics of polyisoprene are approximately coinvariant with tau(beta)(T,P) in order of magnitude to variations of T and P at constant tau(alpha)(T,P). Although this approximate coinvariance property was found before by dielectric relaxation of polar small molecules in mixtures with apolar small molecules or polystyrene, it was rarely found in amorphous polymers. The present finding of the property in polyisoprene extends its generality to polymers.