We present a determination of the nonsinglet transversity parton distribution function (PDF) of the nucleon, normalized with respect to the tensor charge at <math><msup><mi>μ</mi><mn>2</mn></msup><mo>=</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><msup><mrow><mi>GeV</mi></mrow><mrow><mn>2</mn></mrow></msup></math> from lattice quantum chromodynamics. We apply the pseudodistribution approach, using a gauge ensemble with a lattice spacing of 0.094 fm and the light quark mass tuned to a pion mass of 358 MeV. We extract the transversity PDF from the analysis of the short-distance behavior of the Ioffe-time pseudodistribution using the leading-twist next-to-leading order (NLO) matching coefficients calculated for transversity. We reconstruct the <math><mi>x</mi></math>-dependence of the transversity PDF through an expansion in a basis of Jacobi polynomials in order to reduce the PDF ansatz dependence. Within the limitations imposed by a heavier-than-physical pion mass and a fixed lattice spacing, we present a comparison of our estimate for the valence transversity PDF with the recent global fit results based on single transverse spin asymmetry. We find the intrinsic nucleon sea to be isospin symmetric with respect to transversity.