Kim Kardashian showers little North with love while Kanye West pushes the ...

By Iona Kirby

PUBLISHED: 19:01 EST, 7 November 2013 | UPDATED: 21:04 EST, 7 November 2013

She has so far been carried in a convertible car seat that's covered with a blanket on outings with her famous parents.

But North West was instead seen resting against her mother Kim Kardashian's shoulder with her cute face clear for all to see on a family stroll in Santa Barbara on Thursday.

Meanwhile dad Kanye took charge of the stroller as the brood enjoyed a holiday out of Los Angeles together.

This is not only the first time North has been seen in public not covered with a blanket but also the first time we have seen Kim cradling her bundle of joy in such a fashion, and it's clear she is madly in love with her daughter.

The reality star planted kisses on the 20-week-old tot's chubby cheeks while holding North close to her chest.

The family of three were spotted enjoying lunch together, and Kanye tucked into his food while Kim showered their baby girl with affection.

Kim also appeared to be whispering things into North's ear as she cooed over the cute as a button youngster.

Kim, Kanye and North dined al fresco at a pretty restaurant and were seen enjoying bowls of food and Diet Cokes.

The trio had walked to the eatery, with Kim carrying sleeping Nori in her arms as Kanye wheeled the pushchair beside them.

It seems Kim was planning a trip to the gym later in the day, as she was clad in all-black workout wear.

The 33-year-old was sporting trainers, a long-sleeved top and leggings which hugged her famous figure.

Kim appeared to be make-up free for the casual outing, showcasing her natural good looks.

Her fiancé was also wearing gym gear in the form of a grey hoodie, black running shorts and white trainers.

The new parents had dressed North in a cute grey onesie, and the little one's tiny feet were bare.

Kim and Kanye have so far shared just two pictures of North, with the first snap revealed on Kim's mother Kris Jenner's talk show in August.

The second photo was posted on Kim's Instagram page last month.

Kim and Kanye welcomed their daughter into the world on June 15, and got engaged on October 21, Kim's 33rd birthday.

While Kanye was spending quality time with his two favourite girls, his lawyer pleaded not guilty of misdemeanour battery and attempted grand theft on his behalf, in a case filed over a scuffle with a celebrity photographer earlier this year.

Attorney Blair Berk entered the plea for the rapper in a Los Angeles court on Thursday.