NOVELTY - The polyolefin for forming a battery separator, comprises two layers having a first microporous layer material differentiated by a pore size distribution curve having two peaks and a second microporous layer material. The first material comprises a first polyethylene having a molecular weight of 1x 104 to 5x 105, a second polyethylene (7 mass.%) having a molecular weight of less than 1x 106, and a first polypropylene of 25 mass.%. The second material comprises a third polyethylene having a molecular weight of 1x 104 to 5x 105, and a fourth polyethylene (8 mass.%).    USE - The polyolefin is useful for forming a separator useful in the lithium-ion secondary battery.    ADVANTAGE - The polyolefin membrane has improved and well balanced permeability, mechanical strength, heat shrinkage resistance, meltdown properties, electrolytic solution absorption and compression resistance.    DETAILED DESCRIPTION - The polyolefin for forming a battery separator, comprises two layers having a first microporous layer material differentiated by a pore size distribution curve having two peaks and a second microporous layer material. The first material comprises a first polyethylene having a molecular weight of 1x 104 to 5x 105, a second polyethylene (7 mass.%) having a molecular weight of less than 1x 106, and a first polypropylene of 25 mass.%. The second material comprises a third polyethylene having a molecular weight of 1x 104 to 5x 105, a fourth polyethylene (8 mass.%) having a molecular weight of less than 1x 106, and a second polypropylene of 25 mass.%. The polyolefin is present in the form of a multi-layer microporous polyolefin membrane having first, second and third microporous layers. The first and second polyethylenes are high-density-, a medium-density-, a branched low-density- or a linear low-density polyethylene. The second and fourth polyethylenes are an ultra-high molecular weight polyethylene. The pore size distribution curve exhibits a main peak of 0.01-0.08 mu m, and a sub-peak of 0.08-1.5 mu m. INDEPENDENT CLAIMS are included for:    (1) a method for forming a polyolefin; and    (2) a multi-layer, microporous polyolefin membrane.    DESCRIPTION OF DRAWING(S) - The figure shows a graph of typical pore size distribution curve.