TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The basic solution is an aqueous solution of a compound selected from lithium hydroxide, magnesium hydroxide and calcium hydroxide (preferably calcium hydroxide or lithium hydroxide). The catalyst is selected from acid washed activated carbon, calcined sewage sludge solids and silica sand.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Method: The method further involves filtering the triglyceride feedstock before thermal cracking to remove macroscopic contaminant particles. The thermal cracking is conducted at 390 - 460 (preferably 410 - 430)degreesC. The middle distillate fraction is esterified in the presence of methanol as the alcohol or an acid catalyst. The esterifying is conducted at 70 - 120 (preferably 85 - 110)degreesC. The rapid pyrolysis is conducted at 480 - 600 (preferably 550 - 600, especially 565 - 585)degreesC. The triglyceride feedstock is fluidized with steam. The steam to triglyceride feedstock ratio is 0.5 - 1.5 (preferably 0.9). An inert gas (preferably nitrogen) is used to purge any oxidizing agents during rapid pyrolysis. During rapid hydrolysis a catalyst is used to enhance the cracking of triglycerides to largely free fatty acids. Preferred Components: The acid catalyst is selected from sulfuric acid, sulfamic acid, formic acid, acetic acid, propionic acid, hydrochloric acid, phosphoric acid, sulfated metal oxides such as sulfated zirconia, and styrene divinylbenzene copolymers having sulfonic acid functional groups (preferably styrene divinylbenzene copolymer having sulfonic acid functional group). The triglyceride feedstock is selected from restaurant trap grease, rendered animal fats, waste greases and/or low-quality vegetable oils. EXAMPLE - Rendered animal fat having an average density of 0.918 g/ml was fed to a thermal cracking unit, cracked at 411degreesC and atmospheric pressure for 40 minutes. The thermally cracked product contained middle distillates (68.6 wt.%) having a maximum boiling point of 345degreesC, naphtha and the remainder gas, water and residues. The middle distillate stream, having a viscosity of 8.50 cSt, and an acid number of 146.96 mg potassium hydroxide/g, was then fed to an acid esterification unit, where it was contacted with methanol in the presence of Amberlyst 36 (RTM: catalyst). Esterification was conducted at a temperature of 90degreesC and at atmospheric pressure for 20 hours. The resultant raw diesel stream was then treated with a calcium hydroxide solution to produce a final mixed biodiesel/diesel product having an acid number of 0.75 mg potassium hydroxide/g. The biodiesel/diesel product was found to have sulphur (18 ppm) and nitrogen (158 ppm) and a viscosity of 4.84 cSt.