NOVELTY - A separator with heat-resistant insulating layer has a resin porous substrate, and a heat-resistant insulating layer containing heat-resistant particles and binder formed on at least one surface of the resin porous substrate. The heat-resistant particles contain an alpha -alumina. The parameter (X) derived from ratio of alpha -alumina with respect to heat-resistant particles, surface roughness ( mu m) of surface of the heat-resistant insulating layer on opposite side to the resin porous substrate, and thickness ( mu m) of the heat-resistant insulating layer, is 0.018-0.336.    USE - Separator with heat-resistant insulating layer for electrical device (claimed). Uses include but are not limited to lithium ion secondary battery used as power supply for electric vehicles, hybrid electric vehicle, mobile telephone and portable apparatus.    ADVANTAGE - The generation of powder fall-off of heat-resistant particles in heat-resistant insulating layer is suppressed during manufacture of separator, and the short circuit which arises in battery formed using the separator is prevented. The battery has high capacitance and output characteristics.    DETAILED DESCRIPTION - A separator with heat-resistant insulating layer has a resin porous substrate, and a heat-resistant insulating layer containing heat-resistant particles and binder formed on at least one surface of the resin porous substrate. The heat-resistant particles contain an alpha -alumina. The parameter (X) derived from relation: Cax R/D, is 0.018-0.336, preferably 0.07-0.3, where Ca is ratio of alpha -alumina with respect to heat-resistant particles, R is surface roughness ( mu m) of surface of the heat-resistant insulating layer on opposite side to the resin porous substrate, and D is thickness ( mu m) of the heat-resistant insulating layer. An INDEPENDENT CLAIM is included for electrical device.    DESCRIPTION OF DRAWING(S) - The drawing shows cross-sectional schematic view of dipolar type lithium ion secondary battery.    Lithium ion secondary battery (10)    Positive electrode collector (11)    Negative electrode collector (12)    Positive electrode active material layer (13)    Negative electrode active material layer (15)