We use an improved technique to establish new sufficient criteria of product type for the oscillation of the delay differential equation x′(t)+∑l=1mbl(t)x(σl(t))=0,t≥t0,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document} $$\\begin{aligned} x'(t)+\\sum_{l=1}^{m} b_{l}(t)x\\bigl(\\sigma _{l}(t)\\bigr)= 0,\\quad t\\geq t_{0}, \\end{aligned}$$ \\end{document} with b_{l},sigma _{l}in C([t_{0},infty ),[0,infty )) such that sigma _{l}(t)leq t and lim_{t rightarrow infty} sigma _{l}(t)=infty , l=1,2,ldots,m. The obtained results are applicable for the nonmonotone delay case. Their strength is supported by a detailed practical example.