Orthographic processing is characterized by location-invariant and location-specific processing (Grainger, 2018): (1) strings of letters are more vulnerable to transposition effects than the strings of symbols in same-different tasks (location-invariant processing); and (2) strings of letters, but not strings of symbols, show an initial position advantage in target-in-string identification tasks (location-specific processing). To examine the emergence of these two markers of orthographic processing, we conducted a same-different task and a target-in-string identification task with two unfamiliar scripts (pre-training experiments). Across six training sessions, participants learned to fluently read and write one of these scripts. The post-training experiments were parallel to the pre-training experiments. Results showed that the magnitude of the transposed-letter effect in the same-different task and the serial function in the target-in-string identification tasks were remarkably similar for the trained and untrained scripts. Thus, location-invariant and location-specific processing does not emerge rapidly after learning a new script; instead, they may require thorough experience with specific orthographic structures.