Base 4

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:

• kau --> kae-
• motsu --> mote-
• shiru --> shire-
• kaku --> kake-
• oyogu --> oyoge-
• hanasu --> hanase-
• shinu --> shine-
• asobu --> asobe-

For Ichidan verbs, change the final u to e:

• taberu --> tabere-
• miru --> mire-

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?

As a disclaimer, I don't believe a system of "bases" is a good way to learn Japanese verb inflections. It seems to be a rather unnatural way to divide the language. As prime evidence, I offer up this explanation of an imperative inflection:

Contrary to what is stated above this writeup, an imperative inflection of a Japanese verb is not simply formed by this ending. Perhaps I should write a new Japanese Imperative Verb Inflection node, but for the sake of clarity of my argument, here is my understanding of the imperative.

Ichidan or Group I verbs, i.e. those ending with "ru", the uninflected stem of the word is attached to "ro". For example nageru, to throw, becomes nagero.

Godan or Group II verbs, i.e. those ending in a consonant + u, the uninflected stem is attached to "e". For example kaku, to write, becomes kake.

Kuru, to come, being irregular, becomes koi. Suru, to do, becomes shiro.

Also, desu in the conditional form becomes de areba.

Tasukete, stated above as the imperative, is actually the -te form of tasukeru, to help. The imperative is tasukero. The -te is a form that's often used as a shortening of -te kudasai, a request (please do ... for me). This can be seen by reversing the form using the rule above -- it becomes tasuketsu, which by a leap of imagination, could mean majority rule, tasuuketsu (a noun).