We introduce a modified version ƒ_nof the piecewiss linear hisiugrimi uf Beirlant et al. (1998) which is a true probability density, i.e., ƒ_n[d] 0 and [d]ƒ_n=1. We prove that ƒ_nestimates the underlying densitv ƒ strongly consistently in the L₁mmn, derive large deviation inequalities for the t\ error \ƒ_n- f\ and prove that ||/"-/|| tends to zero with the rate n ^-1\3, We also show that the derivative lf'n estimates consistently in ine expected Lx error the derivative/ of sufficiently smooth density and evaluate the rate of convergence n-i/5 for Epf'n -f'% The estimator/" thus enables to approximate/in the Besov space with a guaranteed rate of convergence. Optimization of the smoothing parameter is also studied. The theoretical or experimentally approximated values of the expected errors E\\ƒ_n- f\\ and E||2ƒ'_n-ƒ' are compared with tiie errors aCiiieveu u-y t"e histogram of Beirlant et ah, and other nonparametric methods.