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.