A process for forming a turbine blade for use in high temperature applications, said turbine blade comprising: an as-cast airfoil portion and an as-cast outer tip shroud portion; said outer tip shroud portion having at least two internal cooling passages (16,18) for cooling said outer tip shroud portion, said at least two internal cooling passages (16,18) having at least one exit (22,24,26,28,30,32,34) for discharging cooling air over exterior surfaces of said shroud portion or directly out of the shroud portion, a first of said cooling passages having one cooling fluid exit on a first side of said shroud portion and at least two additional cooling fluid exits (24,26) on a second side of said shroud portion opposed to said first side and a second of said cooling passages has one cooling fluid exit on said second side and at least two additional cooling fluid exits (30,32,34) on said first side, the process comprising the steps of: casting said turbine blade with said as-cast airfoil portion and said as-cast tip shroud: and characterized by: casting said cooling passages (16,18) as as-cast cooling passages (16, 18) within said tip shroud; wherein said casting step comprises casting said first of said as-cast cooling passages with said one cooling fluid exit on said first side of the shroud and said at least two additional cooling fluid exits (24,26) on said second side of the shroud, and casting said second of said as-cast cooling passages with said one cooling fluid exit on said second side and said at least two additional cooling fluid exits (30,32,34) on said first side wherein said airfoil portion casting step comprises using a primary ceramic core to form at least one radial inner passage within said airfoil portion of said turbine blade; and said as-cast cooling passages (16,18) casting step comprises attaching a refractory metal core (102,104) to said primary ceramic core, and wherein said attaching step comprises joining each of said refractory cores (102,104) to said primary ceramic core by inserting at least one tab on each said refractory metal core (102,104) into slot(s) in a tip of the primary ceramic core. an as-cast airfoil portion and an as-cast outer tip shroud portion; said outer tip shroud portion having at least two internal cooling passages (16,18) for cooling said outer tip shroud portion, said at least two internal cooling passages (16,18) having at least one exit (22,24,26,28,30,32,34) for discharging cooling air over exterior surfaces of said shroud portion or directly out of the shroud portion, a first of said cooling passages having one cooling fluid exit on a first side of said shroud portion and at least two additional cooling fluid exits (24,26) on a second side of said shroud portion opposed to said first side and a second of said cooling passages has one cooling fluid exit on said second side and at least two additional cooling fluid exits (30,32,34) on said first side, the process comprising the steps of: casting said turbine blade with said as-cast airfoil portion and said as-cast tip shroud: and characterized by: casting said cooling passages (16,18) as as-cast cooling passages (16, 18) within said tip shroud; wherein said casting step comprises casting said first of said as-cast cooling passages with said one cooling fluid exit on said first side of the shroud and said at least two additional cooling fluid exits (24,26) on said second side of the shroud, and casting said second of said as-cast cooling passages with said one cooling fluid exit on said second side and said at least two additional cooling fluid exits (30,32,34) on said first side wherein said airfoil portion casting step comprises using a primary ceramic core to form at least one radial inner passage within said airfoil portion of said turbine blade; and said as-cast cooling passages (16,18) casting step comprises attaching a refractory metal core (102,104) to said primary ceramic core, and wherein said attaching step comprises joining each of said refractory cores (102,104) to said primary ceramic core by inserting at least one tab on each said refractory metal core (102,104) into slot(s) in a tip of the primary ceramic core.