TECHNOLOGY FOCUS - INSTRUMENTATION AND TESTING - Preferred System: The system further comprises an isolation unit for isolating the hybrid diesel fuel in the third mixture to yield a hybrid diesel fuel product. The isolation unit comprises an H2S stripping unit.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Method: In the method, the hydrotreating involves a hydrotreating catalyst comprising a metal or metal-alloy active hydrotreating catalyst component selected from cobalt-molybdenum (Co-Mo) catalyst, nickel-molybdenum (Ni-Mo) catalyst, and noble metal catalyst. The hydrotreating is carried out at a temperature of 550-800 degrees F under a H2 partial pressure of 400-2000 (preferably 500-1500) psig. The isolation of the hybrid diesel fuel is at least partly achieved by stripping the third mixture of H2S. Preferred Compounds: The first mixture comprises a nitrogen content greater than 50 (preferably up to 500) ppm. The isomerization catalyst comprises Pt on an SM-7 support. The isomerization catalyst comprises Pt on an silicoaluminopihosphate (SAPO)-11 support. The hydrotreating catalyst comprises a refractory oxide support. The hydrotreating catalyst comprises a support component selected from Al2O3 and SiO2-Al2O3. The hydrotreating utilizes an alumina-supported nickel-molybdenum catalyst. The second mixture has, exclusive Of H2S, a sulfur content of not greater than 20 ppm. The second mixture has cloud point of less than or equal to (-8) degrees C. The hybrid diesel fuel has, exclusive Of H2S, a sulfur content of not greater than 10 ppm. The hybrid diesel fuel has a cloud point of less than or equal to (-10) degrees C. Preferred Oils: The vegetable oil comprises at least one biologically-derived oils selected from canola, soy, rapeseed, palm, peanut, jatropha, yellow grease and/or algae. EXAMPLE - Isomerizing a 95/5 diesel/canola oil mixture having approximately 500 ppm sulfur (S), using catalyst of Pt on SM-7, was hydroprocessed (hydrodesulfurization, HDS) in a hydrotreating unit to yield a hybrid diesel intermediate. Then diesel processed with canola oil, this hybrid diesel intermediate mixture was processed in an isomerization unit employing an isodewaxing (IDW) catalyst (Pt on SM-7) to yield a hybrid diesel product having a relatively low cloud point (-13 degrees C).