The order for Hangul is based on the same general principles as Chinese calligraphy:

This applies to both the individual letters and writing out entire blocks composed of multiple letters.

Here are the most basic examples:

Left to Right: The vowel eu

Top to Bottom: The vowel i

Take some time now with a pen and paper to just go through the letters and practice writing them out a few times each.

As long as you get the hang of the general flow it isn't a big deal if you do a few letters in the wrong order. But if you write everything in the wrong order your writing is going to look funny to native speakers.

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