In this work, depithed cardoon stalk (Cynara cardunculus) has been used with the objective of obtaining bleachable pulps. The material, once properly prepared, was subjected to one-step peroxyformic acid delignification. In order to study the process, a face-centred second order factorial design was developed which allowed the determination of the influences of four variables: concentrations of formic acid and hydrogen peroxide in the cooking liquor and the time and temperature of the treatment. Empirical mathematical models have been obtained which predict the yield, kappa index, residual lignin content, and viscosity of the pulps. These models demonstrate that in general the delignification was extensive, producing pulps with kappa indexes less than 25 in the majority of cases, with good yields in the range of 45-60%. However, the pulps seem to have been degraded in the reaction media, as can be deduced from the low viscosity values found: 260-520 mL/g.