Purpose: To unwrap multi-echo phase images for quantitative susceptibility mapping (QSM) in a rapid and robust manner without using complicated search algorithms. Background: Since QSM requires unaliased phase images as input, a reliable 3D phase unwrapping step is essential to reconstruct susceptibility maps. However, this is usually one of the most time-consuming steps in QSM, especially for multi-echo data acquisition. Methods: Strategically acquired gradient echo (STAGE) data are used to provide six flow compensated images with echo times of 2.5 ms, 7.5 ms, 8.75 ms, 12.5 ms, 17.5 ms and 18.75 ms. An unaliased phase image with an effective echo time of 1.25 ms can be created by a complex division between 7.5 ms and 8.75 ms. Using this short pseudo-echo data along with the acquired 2.5 ms data, all other echoes can be unwrapped using a bootstrapping approach. Results: The six echoes (384 × 288 × 64 × 6 voxels) acquired using STAGE data acquisition were unwrapped successfully. This resulted in reliable self-consistent QSM images in only 1 second compared to the quality guided 3DSRNCP algorithm, which took 137 seconds, and the Laplacian based algorithm, which took 23 seconds on the same computer. Conclusions: The proposed bootstrapping multi-echo unwrapping method provides a rapid, robust phase unwrapping method on a voxel-by-voxel basis for online QSM reconstruction.