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Japanese verb base, sometimes known as the "conditional base", because of the few endings that require this base, most of them have some conditional aspect.

To form a Godan verb into Base 4, use the following pattern:

For Ichidan verbs, change the final u to e: Suru becomes sure- in Base 4. Kuru becomes kure- or kore-, depending on the final ending.

A verb in Base 4 with no ending expresses an abrupt command, as in the familiar

Hanase!
Let go!

Tasukete!
Help!

from anime (see? I bet you didn't realize that at the end of the first episode of Princess Rouge, that guy is shouting out a Godan verb in Base 4 no-ending, did you?). In this form, kuru becomes kore, and suru becomes seyo in two-part verbs and is replaced by yaru otherwise.

Two other endings requiring base 4 are -ba (If/When (I) do), and -ba yokatta (it would be better if (I) had done). In both of these forms, kuru becomes kureba and desu becomes naraba.

Kyoo wa watashi ga hayai kaereba, tenisu o shimashoo ka.
If I return early today, shall we play tennis?

Hayaku tabereba yokatta desu.
It would be better if I had eaten early.
I wish I had eaten earlier.

Base 4 + -ru is the Potential Form of Godan verbs. This ending actually creates a new Ichidan verb, which should be further inflected if necessary.

Hanasemasu ka.
Can you speak?